Question

Please Help Me With This Sum ...

Answer 1

Step-by-step explanation:

1) x²+y²= 29, xy= 2

(x+y)²= x²+2xy+y²

(x+y)²= x²+y²+ 2xy

(x+y)²= 29+2*2

(x+y)²= 29+4

x+y = √43. -------------------(1)

2) (x-y)²= x²-2xy+y²

(x-y)²= x²+y²- 2xy

(x-y)²= 29-2*2

(x-y)²= 29-4

x-y = √25. --------------------(2)

3) use expansion formula,

x²+y²= (x+y)²-2xy

(x²)²+(y²)²= (x²+y²)²-2x²y²

equation (1) - equation (2)

x+y = √43

x-y = √25

- + -

________

2y =√18

y = √(18)/2

y = √(18/4)

y = √4.5

y²= 4.5

put y = √4.5 in equation (1)

x+y = √43

x+√ 4.5= √43

x= √43-√4.5

x= √38.5

x²= 38.5

then x²*y² = 38.5*4.5

x²*y² = 173.25

(x²)²+(y²)²= (x²+y²)²-2x²y²

x⁴+y⁴ = 29²-2*173.25

x⁴+y⁴ = 841-346.5

x⁴+y⁴ = 494.5.