Question

if a^2-b^2=36 and a+b=4, then (a-b)^2=---------------

Answer 1

Given that,


a² - b² = 36

And a + b = 4


We know that

a² - b² = (a + b)(a - b)

So by applying this identity in first case we get,

a² - b² = 36

=> (a - b)(a + b) = 36

Now we are given that a + b = 4

=> (a - b)4 = 36

=> (a - b) = 36/4

=> (a - b) = 9


Now we have to find (a - b)²

So substituting the value of a - b we get

(a - b)²

=> (9)²

= 81

So your answer is 81

Hope it helps dear friend ☺️

Answer 2

we know that:
$a {}^{2} - b {}^{2} = (a - b)(a + b)$
given:
$a {}^{2} - b {}^{2} = 36$
&
$a + b = 4$
So we get:
$36 = 4(a - b)$
$a - b = \frac{36}{4} = 9$
Therefore,
$(a - b) {}^{2} = 9 {}^{2} = 81$
Hope this helps:)