Question

a-b=3 a3-b3=117 a+b=?

Answer 1

hey dear

good morning friend.

ur answer goes like this.

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given,

a³ - b³ = 117

=>(a -b) (a² + b² + ab) = 117.

putting,(a - b) = 3,we get

=>3 (a² + b² +ab) = 117

thus,(a² + b² +ab) = 39

now,a² + b² = (a-b)² +2ab

thus, (a -b)² + 3ab = 39

=>(3)² + 3ab = 39

=>9 + 3ab = 39

thus,ab = 10

so,

(a + b)² = (a - b)² + 4ab = 9 + 4 × 10. = 49

thus,

(a + b ) = √49 =+-7 Ans.

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Thanks

Answer 2

➡HERE IS YOUR ANSWER⬇

$Given :\\\\ a - b = 3 .....(i)\\ \\ and\\ \\ a^{3} - {b}^3 = 117 .....(ii)\\ \\ From \:(ii), \:we \:get :\\ \\ {(a - b)}^3 + 3ab(a - b) = 117 \\ \\ or, {3}^3 + 3ab(3) = 117\\ \\ or, 27 + 9ab = 117\\ \\ or, 9ab = 117 - 27\\ \\ or, 9ab = 90\\ \\ or, ab = 10\\ \\ So, we\: have : ab = 10.\\ \\ Now, \:dividing\: (ii)\: by\: (i),\: we\: get :\\ \\ \frac{({a}^3-{b}^3)}{(a - b)}= \frac{117}{3} \\ \\ or, \frac{(a-b)({a}^2+ab+{b}^2)}{a-b} = 39\\ \\ or, {a}^2 + ab + {b}^2 = 39\\ \\ or, {(a+b)}^2 - 2ab+ab=39\\ \\ or, {(a+b)}^2 - ab = 39\\ \\ or, {(a+b)}^2-10 = 39\\ \\ or, {(a+b)}^2 = 49 = {7}^2$

So, either a+b=7 or, a+b=-7

When a-b=3 and a+b=7, a=5 and b=2

When a-b=3 and a+b = -7, a=-2 and b= -5

⬆HOPE THIS HELPS YOU