Question

If x + y = 10 and xy = 4, then what is the value of x4 + y4?

A) 8464 B) 8432 C) 7478 D) 6218

Answer 1

$\huge{\sf{\blue{ANSWER}}}$

GIVEN:-

• x+y=10, xy=4

TO FIND:-

• The value of $x^4+y^4$.

HOW TO SOLVE,

• We have to find the value of $x^2+y^2$

So,

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

$(10)^2=x^2+y^2+8$

$x^2+y^2=92$

As we find the value of $x^2+y^2$ we will square it and find the given value.

$(x^2+y^2)^2=x^4+y^4+2×x^2×y^2$

$x^4+y^4=8464-2(xy)^2$

$x^4+y^4=8464-32$

$x^4+y^4= 8432$

Hence, "B" will be the correct answer.

Answer 2

Hi there!

$\large\sf\underline{Your \:Answer \rightarrow\: B)8432.}$

$\large\sf\underline{Required \: explanation\rightarrow}$

$\bf\green{x + y = 10}$

$\bf\red{{(x + y)}^{2} = {(10)}^{2}}$

$\bf\pink{ {x}^{2} + {y}^{2} + 2xy = {(10)}^{2} }$

$\bf\purple{{x}^{2} + {y}^{2} = 92}$

$\bf\gray{({x}^{2} +{y}^{2} )}^{2} = {(92)}^{2}$

$\bf\orange{8464 - {(2xy)}^{2} }$

$\bf\purple{8464 - 32}$

$\bf\gray{8432}$