Question

x+y=8 and xy=9 find the value of x³+y³​

Answer 1

Question

x+y=8 and xy=9 find the value of x³+y³​

Step-by-step explanation:

x+y=8

xy=9

x³+y³​=?

(x+y)³ = x³ + y³ + 3xy (x+y)

⇒ 8³ = (x³ + y³) + 3× 9×8

⇒ 512 = (x³ + y³) +216

⇒ 512-216 = x³ + y³

⇒x³ + y³ = 296

Answer 2

$\large\sf\underline{✰\:Given}$

• $\sf\:x+y=8$

• $\sf\:xy=9$

$\large\sf\underline{✰\:Solution}$

• We know

$\tt\red{(x+y)^{3}=x^{3}+y^{3}+3xy(x+y)}$

$\tt\red{∴x^{3}+y^{3}=(x+y)^{3}-3xy(x+y)}$

$\sf⇒\:x^{3}+y^{3}=8^{3}-3(9)(8)$

$\sf⇒\:x^{3}+y^{3}=512-27 \times 8$

$\sf⇒\:x^{3}+y^{3}=512-216$

$\sf⇒\:x^{3}+y^{3}=296$

• Thnku ❣