Question

x^4+y^4=19,x+y=1,findx^2y^2-2xy

Answer 1

hope the answer helped u

Answer 2

The value of x²y²-2xy is 9

Given,

x⁴+ y⁴ = 19

x+y= 1

Find,

We have To Find the value of x²y²-2xy

Solution,

x⁴+ y⁴ + 2x²y² = 19 + 2x²y²

[ We add 2x²y² both side of equation]

or, x⁴+ y⁴ + 2x²y²- 2x²y² = 19

or, (x²+y²)²= 19 + 2x²y²

or, (x²+y²-2xy+ 2xy) = 19 + 2x²y²

or, [(x+y)²- 2xy]²= 19 + 2x²y²

or, (1-2xy)²= 19 + 2x²y²

or, 1+ 4x²y² - 4xy = 19 + 2x²y²

or, 1+ 4x²y² - 4xy- 2x²y² = 19

or, 4x²y² - 4xy- 2x²y² = 18

or, 2x²y²- 4xy = 18

or, 2( 2x²y²- 2xy) = 18

or, 2x²y²- 2xy = 18/2

or, 2x²y²- 2xy = 9

Hence, the value of x²y²-2xy is 9

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