Question

X+y=1 ,xy(xy-2)=12 thn find x^4+y^4​

Answer 1

Answer:

$:x^4+y^4=25$

Step-by-step explanation:

X+y=1 ,xy(xy-2)=12 thn find x^4+y^4​

Formula used:

$(a+b)^2=a^2+b^2+2ab$

$(a-b)^2=a^2+b^2-2ab$

Given:

$x+y=1$.......(1)

$xy(xy-2)=12$.....(2)

consider

$x+y=1$

squaring on both sides

$(x+y)^2=1^2$

$x^2+y^2+2xy=1$

$x^2+y^2=1-2xy$

squring once again

$(x^2+y^2)^2=(1-2xy)^2$

$\implies\:x^4+y^4+2x^2y^2=1+4x^2y^2-4xy$

$\implies\:x^4+y^4=1+2x^2y^2-4xy$

$\implies\:x^4+y^4=1+2xy(xy-2)$

$\implies\:x^4+y^4=1+2(12)$ (using (2))

$\implies\:x^4+y^4=1+24$

$\implies\:x^4+y^4=25$