Question

x^2+y^2 = 13 and xy= 6 find x^3+y^3

Answer 1

x²+y²=13

(x+y)²=x²+y²+2xy

(x+y)²=13+12

(x+y)²=25

x+y=5

(x+y)³=x³+y³+3xy(x+y)

125=x³+y³+3(6)(5)

125=x³+y³+90

x³+y³=35

Hope it helps

Answer 2

Answer :

x³ + y³ = 35

Explanation :

Given,

$\sf \: {x}^{2} + {y}^{2} = 13 \: and \: xy = 6$

To finD

$\sf \: {x}^{3} + {y}^{3}$

Firstly,we would need to find the value of x + y

Here,

$\sf(x + y) {}^{2} = {x}^{2} + {y}^{2} + 2xy \\ \\ \longmapsto \: \sf \: {(x + y)}^{2} = 13 + 2(6) \\ \\ \longmapsto \: \sf \: {(x + y)}^{2} = 25 \\ \\ \longmapsto \: \boxed{ \sf{x + y = 5}}$

Now,

$\sf \: {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y) \\ \\ \longmapsto \: \sf \: {5}^{3} = {x}^{3} + y {}^{3} + 3(6)(5) \\ \\ \longmapsto \sf 125 = {x}^{3} + {y}^{3} + 90 \\ \\ \longmapsto \: \boxed{\sf { {x}^{3} + {y}^{3} = 35 }}$