Question

If a + b = 11, a2 + b2 = 61, find a3 + b3.

Answer 1

(a+b)^2=a^2+b^2+2ab
=> (11)^2=61+2ab
=> 2ab = (121-61)
=> 2ab = 60
=> ab= 30
now
(a+b)^3=a^3+b^3+3ab (a+b)
(11)^3=a^3+b^3+3×30×11
=> a^3+b^3= 1331- 990
=> a^3+b^3= 341.

Answer 2

Answer:

$a^{3}+b^{3}=341$

Step-by-step explanation:

Given: $a+b=11, a^{2}+b^{2}=61$, then

$(a+b)^{2}=a^{2}+b^{2}+2ab$

Putting the given values, we get

$(11)^{2}=61+2ab$

$121-61=2ab$

$ab=30$

Now, $a^{3}+b^{3}=(a+b)(a^{2}+b^{2}-ab)$

$a^{3}+b^{3}=(11)(61-30)$

$a^{3}+b^{3}=341$