THE EQUATION OF TRANSFORMATION

Class 11th RD Sharma plays a significant role in advanced mathematics, and in order to transform an equation, it is necessary to determine the relation between two square roots and the needed roots, so that the transformation can be applied. In order to get an equation transformed the reciprocal value of the equation needs to be substituted with 1/x. It is necessary to take into consideration that equations whose roots are going negative, it is essential to replace the X with -x. Moreover, the equation to transform to a different equation whose square roots have been mentioned is to be replaced with √x. Furthermore, in the case of an equation whose roots cubes in the given equation, then are x is substituted with the cube root of x. 

CONCEPT OF EQUATION OF TRANSFORMATION

A transformation equation may be defined as an equation transforming into one equation to another whose given roots are inverse to the roots present in an equation that is given. It is necessary to simplify this transformation process to get an idea of the equation of transformation. In advanced mathematics, RD Sharma class 11th solutions have tried to provide in-depth knowledge to the students of class 11, by simplifying the concept of the transformation with the help of equations. Considering x to be a given equation and y being a root connecting the transformed equation, there is a transformed equation that is to be obtained by putting as convention x= – y in f(x) = 0. Therefore, it is required to consider x to be the root of the mentioned equation, and y to be that transformed equation’s root.  

It is not possible to explain a transformation equation without showing how the transformation happens into another equation whose given roots are inverse or reciprocal to the roots of an equation that is given. 

There is a practical example from mathematics of class 11th by RD Sharma of how the transformation takes place:

Let   f(x) =a0xn +a1xn-1 +a2xn-2 +…+an-1x + an =0   be the given equation. Then, y=1/x

Or, x=1/y”

By putting the value x=1/y in the equation, the following solution can be achieved:

Au/yen +a1/ yn-1 + a2/yn-2 + …an-1/y + an = 0

Or, any + an-1 + an-2yn-2 +…+ a1y + au =0

Therefore, it is observed that to get an equation containing roots that are reciprocal to the roots of an equation that is given, it is necessary to replace it with 1/x in the above equation that is given or will be considered in the future.

DISCUSSION OF EQUATION OF TRANSFORMATION

Class 11th RD Sharma deals with solutions that help to understand the equation of transformation. Transformation may be defined as an intricate procedure that causes the manipulation of a polygon or 2D object on a geometric plane or coordinate plane. To explain it in a more lucid language transformation involves the inversion of an image to give a two-dimensional view before the change or transformation is initiated. The book has a separate chapter on the understanding of the equation of transformation which consists of questions and sub-questions to help the students.

RD Sharma in his book has discussed how to apply formulas so that the values of sines and cosines can be transformed. It is essential to understand the basic formulas of trigonometry to get an idea or grip about the equation of transformation. It is necessary to cover the formulas of sine and cosine to apply the formulas to provide a balanced equation on both sides. As a convention, it is required to balance the right-hand side of the question with the left-hand side. To balance both sides, it is necessary to identify and understand which formula needs to be applied in the given problem. Class 11th RD Sharma has made the transformation simpler for the students of the 11th standard as he has successfully simplified the understanding of the equation of transformation. RD Sharma class 11th consists of numerous questions based on the application of the transformation problems which will make the students confident and capable during the time of their examinations.  

CONCLUSION

Class 11th RD Sharma provides a clear explanation regarding transformation formulas and how they can be applied in higher mathematics to provide solutions to mathematical problems. The solutions are already given in the book using lucid language and multiple steps to enable the students to understand the matter and develop proficiency while solving the mathematics of class 11th by RD Sharma that involve transformation formulas. The question given on the exercise portion will allow the students to understand how to transform the product into addition or subtraction. Furthermore, the reverse action of transformation from the sum or difference can also be performed. In addition to this, RD Sharma class 11th related to trigonometry also serves as a  guidebook to make the students understand how transformation formulas can be applied in mathematical questions they will come across in their entrance as well as onboard examinations such as JEE Advanced and JEE Mains.