Question

if x+y=8 and xy=15 then find the value of x⁴+x²y²+y⁴​

Answer 1

Answer:

-29

Step-by-step explanation:

xy=15

so (xy)^2=15*15=225

x+y=8

(x+y)(x+y)=8*8=64

x^2+y^2+2xy=64

x*x + y*y = 64-(2*15)=64-30=14

(x^2+y^2)(x^2+y^2)=14*14=196

x^4 + y^4 + 2(x^2)(y^2) = 196

x^4 + y^4 + 2(225) = 196

x^4 + y^4 = 196-450

x^4 + y^4 + (x^2)(y^2) = 196-225-225+225 = 196-225

=-29

Answer 2

Answer:931

Step-by-step explanation:

Given that,

x+y=8..............(1)

And xy=15......(2)

To find value of x^4+x^2y^2+y^4=?

From (2), x^2y^2=(15)^2=225

Squaring (1) we get

(x+y)^2=8^2

Or,x^2+y^2+2xy=64

Or,x^2+y^2+2×15=64

Or, x^2+y^2=64-30

Or, x^2+y^2=34..............(3)

Squaring (3) we get

(x^2+y^2)^2=(34)^2

Or, x^4+y^4+2x^2y^2=1156

Or, x^4+y^4+2×225=1156

Or,x^4+y^4=1156-450

Or, x^4+y^4=706

Therefore,

x^4+y^4+x^2y^2=706+225=931