Question

a-b=4
a+b=6
find
$( i) \: \: {a}^{2} + {b}^{2}$
$(ii) \: \: ab$

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Answer 1

Given :-

a - b = 4 - [1]

and

a + b = 6 - [2]

On adding Equation 1 and 2 , We get

a - b + a + b = 4 + 6

=> 2a = 10

=> a = 5

Now putting this value of a in equation 1 we get ,

5 - b = 4

=> 5 - 4 = b

=] 1 = b

So , a² + b² = (5)² + (1)² = 25 + 1 = 26

and ab = 5 x 1 = 5

Hope it helped...

Answer 2

Given :-

a - b = 4 - [1]

and

a + b = 6 - [2]

On adding Equation 1 and 2 , We get

a - b + a + b = 4 + 6

=> 2a = 10

=> a = 5

Now putting this value of a in equation 1 we get ,

5 - b = 4

=> 5 - 4 = b

=] 1 = b

So , a² + b² = (5)² + (1)² = 25 + 1 = 26

and ab = 5 x 1 = 5

Hope it helped...

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