Question

If x + y = 5 and x^ 2 +y^ 2 =13, then x ^ 6 - y ^ 6 equals (Assume x X >; y)

Answer 1

Answer: The value of $x^6 - y^6$ is 665

Step-by-step explanation:

Given:

$x+y = 5$

$x^2 + y^2 = 13$

$x>y$

We know that:

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

$(5)^2 = 13+2xy$

$25-13 = 2xy$

$12 = 2xy$

$xy = 6$

Now,

$x + y = 5$ ;  $xy = 6$ ;  $x>y$

∴ $x = 3, y = 2$

To find: $x^6 - y^6$

$x = 3, y = 2$

$(3)^6 - (2)^6$

$= 729 - 64$

$= 665$

Answer: The value of $x^6 - y^6$ is 665

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