Question

if x²+y²=4xy, let's prove that x⁴+y⁴=14x²y²​

Answer 1

Answer:

squaring on both sides

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

x^4+y^4+2=16x^2×y^2

x^4+y^4=16x^2y^2-2

x^4+y^4=14x^2y^2

Answer 2

Answer:

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

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

$16 {x}^{2} {y}^{2} = {x}^{4} + {y}^{4} + 2 {x}^{2} {y}^{2}$

$16 {x}^{2} {y}^{2} - 2 {x}^{2} {y}^{2} = {x}^{4} + {y}^{4}$

$14 {x}^{2} {y}^{2} = {x}^{4} + {y}^{4}$

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