Question

If a+b=15 and a^2+b^2=60, what is the value of a-b?

Answer 1

Given:  a+b = 15   and  $a^{2} -b^{2} = 60$

To find:  Value of a - b

Solution:

We know the formula   $a^{2} - b^{2} = (a+b)(a-b)$

By substituting the given values, we get:

⇒ 60 = 15(a - b)

⇒ a - b = 60/15

⇒ a - b = 4

The value of a - b is 4

Answer 2

Answer:

Value of a-b is $\sqrt{-105}$

Step-by-step explanation:

We are given that

a+b =15

$a^2+b^2=60$

If we try to find the square of a+b=15

We will get

$(a+b)^{2} =15^{2} \\a^{2} +b^{2} +2ab=225$

Now we are also given $a^2+b^2=60$ if we put this, we will get

60+2ab=225

2ab=225-60

2ab=165

Now we know that

$(a-b)^{2} = a^{2} +b^{2} -2ab\\(a-b)^{2} =60-165\\(a-b)^{2} =-105\\a-b=\sqrt{-105}$