Question

If a²+b²=41 and ab=4 then find a-b

Answer 1

Given:

a²+b² = 41

ab = 4

Proof

We know that:

( a - b)²

==> (a-b)(a-b)

==>a(a-b) - b(a-b)

==> a² - ab - ab + b²

==> a² + b² - 2 ab........................(1)

Thus:

(a - b)² = a² + b² - 2ab

Solution

( a - b )² = 41 - 2*4

==> (a-b)² = 41 -8

==> (a-b)² = 33

a-b = √33

or a-b = -√33

There are two answers:

√33 or -√33

Hope it helps you

__________________________________________________________________

Answer 2

$\bold{ANSWER}$


$\underline{GIVEN}$


a² + b² = 41


ab = 4


$\underline{\:TO\:FIND}$


a - b = ?


$\underline{SOLUTION}$


We know that


( a - b )² = a² + b² - 2ab


=> ( a - b )² = 41 - 2( 4 )


=> ( a - b )² = 41 - 8


=> ( a - b )² = 33


=> By taking square root on both the sides


=> a - b = √33. or. a - b = - √33