Question

if a + b is equals to 3 and a square + b square is equal to 40 find the value of a cube plus b cube​

Answer 1

Answer:

here is the answer....two identities have been used in the question..

1. ${(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \\ {a}^{3} + {b}^{3} = (a + b)( {a}^{2} + {b}^{2} - ab )$

Answer 2

The value of a³+b³ is 166.5.

Explanation:

Given : a+b= 3 and a²+b²= 40

To find : a³+b³

Consider , a+b= 3

Squaring on both sides , we get

(a+b)² = (3)²

⇒ a²+b²+2ab = 9

Substitute value of a²+b² , we get

⇒ 40 +2ab=9

⇒ 2ab = 9-40=-31

⇒ $ab=\dfrac{-31}{2}$

Since , $a^3+b^3=(a+b)(a^2+b^2-ab)$

$=(3)(40-\dfrac{-31}{2})=(3)(40+\dfrac{31}{2})=\dfrac{333}{2}=166.5$

Hence, the value of a³+b³ is 166.5.

# Learn more :

Which calculation can be used to find the value of q in the equation q3 = 64?

a) q equals square root of 64 over 3

b) q equals square root of 64

c) q equals cube root of 64

d) q equals 3 multiplied by square root of 64

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