Question

If |a+b | = |a - b | prove that ā and b are perpendicular.​

Answer 1

Answer:

Ques. : Prove that -

{(a + b)}^{2} \: - {(a - b)}^{2} = 4ab(a+b)

2

−(a−b)

2

=4ab

Sol. :

{(a + b)}^{2} \: - {(a - b)}^{2}(a+b)

2

−(a−b)

2

= ( {a}^{2} + 2ab + {b}^{2} ) - ( {a}^{2} - 2ab + {b}^{2} )(a

2

+2ab+b

2

)−(a

2

−2ab+b

2

)

= {a}^{2} + 2ab + {b}^{2} \: - {a}^{2} + 2ab - {b}^{2}a

2

+2ab+b

2

−a

2

+2ab−b

2

= 4ab4ab

------ (PROVED)

HOPE, it help you.