Question

If a=117+b^3 and a=3+b, then find the value of a+b?
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Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Solution: a³=117+b³ and a=3+b

a^3-b^3 = 117, or

(a-b)(a^2+ab+b^2) = 117 …(1)

a=3+b or a-b = 3 …(2)

Hence (1) becomes 3(a^2+ab+b^2) = 117, or

a^2+ab+b^2 = 39, or

a^2+2ab-ab+b^2 = 39

(a+b)^2 - ab = 39, or

(a+b)^2 = 39+ab, or

a^2+2ab+b^2 = 39+ab …(3)

(a-b)^2 = 3^2 = 9, or

a^2–2ab+b^2 = 9 …(4)

Subtract (4) from (3)

4ab = 30+ab or

3ab = 30, or

ab = 10.

(3) becomes (a+b)^2 = 39+10 = 49, or

a+b = ±7. Answer.