Question

Given a -­ b = 2, a3 - b3=26 then (a + b)2 is

A) 9 B) 4 C) 16 D) 12

Answer 1

Answer:

b

Step-by-step explanation:

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Answer 2

Answer:

C) 16

Step-by-step explanation:

Given:

$a - b = 2$

${a}^{3} - {b}^{3} = 26$

There are two cubic formulas

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

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

From second cubic formula,

$26 = 8 + 6ab$

$ab = 3$

From the first cubic formula,

$26 = 2( {a}^{2} + {b}^{2} + ab)$

$13 = {a}^{2} + {b}^{2} + 3$

${a}^{2} + {b}^{2} = 10$

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

$= 10 + 2(3) = 16$