Question

If x2+y2=1then( 3x-4y3)2+(3y-4y3)2=
​

Answer 1

Answer:

1

Step-by-step explanation:

Given : x²  + y² = 1

=> 4x² = 4 - 4y² and 4y² = 4 - 4x²

(4x³ - 3x)² + (3y - 4y³)²

= [ x * (4x² - 3) ]² + [ y * (3 - 4y²) ]²

=  x² * (4 - 4y² - 3)² +  y² * (3 - 4 + 4x²)²

=  x² (1 - 4y²)² +  y² (4x² - 1)²

=  x² (1 + 16y^4 - 8y² ) +  y² (16x^4 + 1 - 8x²)

=  x² + 16x²y^4 - 8x²y² +  16x^4 y² + y² - 8x²y²

=  (x² + y²) + 16x²y² ( x² + y²) - 16x²y²

= 1 + 16x²y² - 16x²y² . . . {As  x² + y² = 1 }

=> 1 ===> ANS