Question

Find x^4+y^4 if x-y=7 and xy=9

Answer 1

Answer:

= > x - y = 7

Square on both sides:

= > ( x - y )^2 = 7^2

= > (x)^2 + (y)^2 - 2(x)(y) = 49

= > x^2 + y^2 - 2xy = 49

xy = 9

= > x^2 + y^2 = 49 + 2xy = 49 + 2(9)

= > x^2 + y^2 = 49 + 18 = 67

Square on both sides :

= > ( x^2 + y^2 )^2 = 67^2

= > x^4 + y^4 + 2(xy)^2 = 4489

= > x^4 + y^4 = 4489 - 2(9)^2

= > x^4 + y^4 = 4489 - 162

= > x^4 + y^4 = 4327

Required value is 4327

Answer 2

X-Y =7

Squaring both sides ,we get

➜ (x - y) ^2 = 7^2

➜ (x) ^2 + (y)^2 - 2 .x.y = 49

➜ x^2 + y^2 - 2xy =49

➜ xy = 49

➜x^2 + y^2 = 49 + 2xy = 49 + 2(9)

➜ x^2 +y^2 = 49 + 18 = 67

Square the both sides,

➜ (x^2 + y^2)^2 = 67 ^2

➜ x^4 + y^4 + 2x(y) ^2 = 4489

➜ x^4 + y^4 = 4489 - 2(9)^2

➜ x^4 + y^4 = 4489 - 162

➜ x^4 + y^4 = 4327

Required answer is 4327.