Question

If a - b is = 4 and a+ b= 6 find: a2+ b2 , ab​

Answer 1

a-b=4

a=4+b

a+b=6

4+b+b=6

4+2b=6

2b=6-4

2b=2

b=2/2

b=1

Now

b=1

we know

a-b=4

a-1=4

a=4+1

a=5

We got

A=5

B=1

Then

(1)a²+b²

5²+1²

25+1

=26

(2)ab

5×1

=5

$\boxed{\mathbf{\huge{{a}^{2}+{b}^{2}=26}}}$

$\boxed{\mathbf{\huge{ab=5}}}$

Answer 2

Solution:-

Given:-

( a - b) = 4.

& ( a + b) = 6.

Given that ( a + b) = 6

=) a + b = 6.

Squaring on both the sides. we get,

=) ( a+b)² = 6²

=) (a + b)² = 36--------(1).

Case ||,

( a - b) = 4

Squaring on both the sides. we get,

=) ( a-b)² = 4²

=) ( a-b)² = 16--------(2).

Adding Eq(1) and Eq(2). we get,

=) (a + b)² + ( a-b)² = 36 + 16

=) a² + b² + 2ab + a² + b² - 2ab = 52

=) 2a² + 2b² = 52

=) a² + b² = 52/2

=) a² + b² = 26.

Now,

Given Equations;

a - b = 4

=) a = b + 4---------(3).

Putting ( a = b+4) in ( a+b = 6).

=) a + b = 6

=) b + 4 + b = 6

=) 2b = 6-4

=) b = 1.

Putting ( b=1) in eq(3).

=) a = 1 + 4

=) a = 5.

Hence,

ab = 5.