Question

If a3 + b3 = 35 and ab = 6, then what is the value of a + b?

A) 5 B) 8 C) 2 D) -8

Answer 1

The answer is A.5

Step-by-step explanation:

we know that-

a³+b³=(a+b)(a²-ab+b²)

35= (a+b)(-ab+(a+b)²-2ab)

[using identity: (a+b)²=a²+b²+2ab]

35=(a+b)(-3ab+(a+b)²)

35=(a+b)(-3×6+(a+b)²)

35=(a+b)(-18+(a+b)²)

35= -18(a+b)+(a+b)³

Put a + b = x

⇒ x3 – 18x – 35 = 0

Using trial error method,

(Trick: Put values of x as given in the options)

Putting x = 5

L.H.S. = 125 – 90 – 35 = 0 = R.H.S.

∴ a + b = 5

Hope it helps!

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