Question

Question given below
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Answer 1

Answer:

741

Step-by-step explanation:

x= 2

y= 5

2+5= 7

2×5= 10

${2}^{4} + {2}^{2} \times {5}^{2} + {5}^{4} = 741$

Answer 2

$\Large\underline\mathsf{Given:-}$

$x + y = 7$

$xy = 10$

$\Large\underline\mathsf{To \: find:-}$

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

$\Large\underline\mathsf{Solution:-}$

$x + y = 7$

Square on both sides:-

${(x + y)}^{2} = {7}^{2}$

${x}^{2} + {y}^{2} + 2xy = 49$

${x}^{2} + {y}^{2} = 49 - 20$

${x}^{2} + {y}^{2} = 29$

Now,

$xy = 10$

Square on both sides:-

${x}^{2} {y}^{2} = 100$

Now, we have to find x⁴ and y⁴

So,

${x}^{2} + {y}^{2} = 29$

Square on both sides:-

$( { {x}^{2} + {y}^{2}) }^{2} = 841$

${x}^{4} + 2 {x}^{2} {y}^{2} + {y}^{4 } = 841$

put the value of x²y²=100

${x}^{4} + {y}^{4} = 841 - 200$

${x}^{4} + {y}^{4} = 641$

Now, we get our answer,

${x}^{4} + {x}^{2} {y}^{2} + {y}^{4} = 641 + 100$

${x}^{4} + {x}^{2} {y}^{2} + {y}^{4} = 741$

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