Question

If x+2y = 10, XY= 15, find x^3+ 8y

Answer 1

$\large{\boxed{\bold{Answer:}}}$

x+2y = 10 (i)

xy = 15 (ii)

Identity:

$(x + y {)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y) \\ \\ = (x + 2y {)}^{3} = {x}^{3} \: +(2y {)}^{3}+ 3(x)(2y)(x + 2y) \\ \\ = (10 {)}^{ 3 } = {x}^{3} + 8 {y}^{3} + 6 \times 15(10) \\ \\ = (1000) = {x}^{3} + 8 {y}^{3} + 900 \\ \\ = 1000 - 900 = {x}^{3} + 8 {y}^{3} \\ \\ = {x}^{3} + 8 {y}^{3} = 100$

$\large{\boxed{\bold{Hope\:it\:helps\:you!}}}$

Answer 2

Heya!!

Thanks for asking the question!

Answer : 100

Explanation :

Given,

x + 2y = 10

xy = 15

To find,

x^3 + 8y^3

We know the identity,

(a + b)^3 = a^3 + b^3 +3ab(a + b)

Here in this case,

a = x

b = 2y

a + b = 10

ab = 15

a^3 + b^3 = ?

Now, substituting the values in the identity, we get : -

(10)^3 = x^3 + 8y^3 + 90(10)

1000 = x^3 + 8y^3 + 900

x^3 + 8y^3 = 1000 - 900

x^3 + 8y^3 = 100. ( Answer )



Hope it helps you.