JEE Class main Answered
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Asked by j.nagaraji1983 | 24 Oct, 2023, 10:53: AM
![begin mathsize 14px style x squared plus y squared space equals space t space plus space 1 over t end style](https://images.topperlearning.com/topper/tinymce/cache/ea432a20c4f361bd6b5ae07f12910b99.png)
![begin mathsize 14px style open parentheses x squared plus y squared close parentheses squared space equals space open parentheses t space plus space 1 over t close parentheses squared space equals space t squared plus 1 over t squared plus 2 end style](https://images.topperlearning.com/topper/tinymce/cache/8a3e17287884ff514cb5c0c2188df368.png)
Expanding LHS and substituting for ( t2 + 1/t2 ) = x4 + y4 , we get
![begin mathsize 14px style x to the power of 4 plus y to the power of 4 plus 2 space x squared y squared space equals space x to the power of 4 plus y to the power of 4 to the power of space end exponent plus space 2 end style](https://images.topperlearning.com/topper/tinymce/cache/7f05764316e77467d4965681b98be252.png)
From above expression we get
![begin mathsize 14px style x squared y to the power of 2 to the power of space end exponent space equals space 1 end style](https://images.topperlearning.com/topper/tinymce/cache/a450c85f2737305aec692e031a7d4f3b.png)
By differentiating above expression on both sides, we get
![begin mathsize 14px style x squared space 2 space y space fraction numerator d y over denominator d x end fraction space plus space y squared space left parenthesis 2 x right parenthesis space equals space 0 end style](https://images.topperlearning.com/topper/tinymce/cache/b060ebc9467495fc7961b40e309839a6.png)
From above expression, we get
![begin mathsize 14px style x space fraction numerator d y over denominator d x end fraction space equals space minus y end style](https://images.topperlearning.com/topper/tinymce/cache/5baf5cef2c4b164241f0b7e9beb17958.png)
If we mulitply both sides of above expression by x2y , we get
![begin mathsize 14px style x cubed y space fraction numerator d y over denominator d x end fraction space equals space minus x squared y squared end style](https://images.topperlearning.com/topper/tinymce/cache/a9bd9d6977acd17f2762fb8417d23c42.png)
Usine eqn.(1) , we re write the above expression as
![begin mathsize 14px style x cubed y space fraction numerator d y over denominator d x end fraction space equals space minus space 1 end style](https://images.topperlearning.com/topper/tinymce/cache/f4e0ef857ea872053d99453cac23f1b9.png)
Answered by Thiyagarajan K | 24 Oct, 2023, 14:56: PM
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