Question

of x² + y² = 29 and xy =2, find x^4+y^4

Answer 1

your ans = 833

( x² + y²)² = (x²)² + (y²)² + 2x²y².

= x⁴ + y⁴ + 2 (xy) (xy).

(29)² = x⁴ + y⁴ + 2 (2) (2).

841. = x⁴ + y⁴ + 8.

so, x⁴ + y⁴ = 841 - 8.

x⁴ + y⁴ = 833.

Answer 2

$\sf{\huge{\underline{\green{Given :-}}}}$

• x² + y² = 29

• xy =2

$\sf{\huge{\underline{\green{To\:Find :-}}}}$

• ${x}^{4} + {y}^{4}$

$\sf{\huge{\underline{\green{Answer :-}}}}$

We have to find,

${x}^{4} + {y}^{4}$

➝ ${x}^{4} + {y}^{4}$ = $( {x}^{2} + {y}^{2} )^{2}$

➝ $( {x}^{2} + {y}^{2} )^{2}$ = ${x}^{4} + 2 {x}^{2} {y}^{2} + {y}^{4}$

➝ ${x}^{4} + {y}^{4}$ = ${x}^{4} + 2 {x}^{2} {y}^{2} + {y}^{4}$

➝ ${x}^{4} + {y}^{4}$ = $( {x}^{2} + {y}^{2} ) ^{2} - 2 {x}^{2} {y}^{2}$

➝ ${x}^{4} + {y}^{4}$ = $({x}^{2} + {y}^{2})^{2} - 2(x y)^{2}$

We have,

x² + y² = 29

xy =2

➝ ${x}^{4} + {y}^{4}$ = (29)² - 2(2)²

➝ ${x}^{4} + {y}^{4}$ = 29×29 - 2×2 ×2

➝ ${x}^{4} + {y}^{4}$ = 841 - 8

➝ ${x}^{4} + {y}^{4}$ = 833

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