Question

If a + b equals to 11 a square + b square equal to 61 find a cube plus b cube

Answer 1

Answer:

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Answer 2

Answer:

Given: a+b=11.................(1)

And a^2+b^2= 61...........(2)

To find: a^3+b^3=?

Now we know,

(a^3+b^3)=(a+b) (a^2-ab+b^2).............(3)

From (1),

(a+b)^2= 11^2

Or,a^2+2ab+b^2=121

Or, (a^2+b^2)+2ab=121

Or, 61+2ab=121

Or, 2ab= 121-61

Or,2ab= 60

Hence, ab= 30

Now, using this in equation (3), we get

(a^3+b^3) = (a+b)(a^2+b^2-ab)

= 11 (61-30)

= 11*31

=341.

This is the required answer.