Question

if (a+b) = 5 and (a-b) = 3, then a^2-b^2= ?

Answer 1

Answer:

$a + b = 5 \\ a - b = 3 \\ - - - - - \\ 2a = 8 \\ a = \frac{8}{2} \\ \boxed{a = \underline{ \underline{4}}} \\ \\ a - b = 3 \\ 4 - b = 3 \\ 4 - 3 = b \\ \boxed{ \underline{ \underline{1}} = b} \\ \\ {a}^{2} - {b}^{2} \\ = {4}^{2} - {1}^{2} \\ = 16 - 1 \\ \large{ \boxed{= \underline{ \underline{15}}}}$

Answer 2

SOLUTION

GIVEN

a + b = 5 & a - b = 3

TO DETERMINE

The value of a² - b²

FORMULA TO BE IMPLEMENTED

We are aware of the identity that

$\sf{ {a}^{2} - {b}^{2} = (a + b)(a - b) }$

EVALUATION

Here it is given that a + b = 5 & a - b = 3

Now

$\sf{ {a}^{2} - {b}^{2} }$

$\sf{ = (a + b)(a - b) }$

$\sf{ = 5 \times 3 }$

$\sf{ = 15 }$

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