Math, asked by arakanumerasu, 1 year ago

If x root (1+y) + y root (1+x) = 0 Prove that dy/dx = -1/(1+x)2 experts do help!!

Answers

Answered by kvnmurty
59
x √(1+y)  +  y √(1+x) = 0
x √(1+y) = - y √(1+x)
square on both sides:
    x² (1+y) = y² (1+x)
    y² (1+x) - x² y  - x² = 0
    y = [ x² + √(x⁴+4x+4x³) ] / [2(1+x)]
       = [x² + x(x+2) ] /[2(1+x)]

    y  = x  or   -x / (1+x)

or,  y = x   or    -1 + 1/(1+x) 

Differentiate wrt x:   
     dy/dx = 1   or    -1/(1+x)²
 

kvnmurty: click on red heart thanks above pls
Answered by AspiringLearner
2

Please find the attached image. It has a detailed solution with steps. Hope it helps.

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