Question

-- 8. If a2 + b2 = 42 and ab = 4, find the a²-b²
​

Answer 1

Answer:

Formula (a+b)

2

=a

2

+b

2

+2ab

Given, a

2

+b

2

=41 and ab=4

So, (a+b)

2

=a

2

+b

2

+2ab=41+2×4=41+8=49

=>a+b=

49

=7

Answer 2

Answer:

The answer is $10\sqrt{17}$

Step-by-step explanation:

Given $a^2+b^2=42$ and $ab=4$

Using $(a-b)^2=a^2+b^2-2ab$

        $\Rightarrow (a-b)^2=42-2(4)=42-8=34\\\Rightarrow a-b=\sqrt{34}$

And using $(a+b)^2=a^2+b^2+2ab$

                 $\Rightarrow (a+b)^2=42+2(4)=42+8=50\\\Rightarrow a+b=\sqrt{50}=5\sqrt 2$

Therefore $a^2-b^2=(a+b)(a-b)$

                             $=5\sqrt {2}\times \sqrt{34}=5\sqrt{68}\\=5\sqrt{4\times 17}=5\sqrt 4\times \sqrt{17}=10\sqrt{17}$