Question

If A is the A.M between a and b , prove that 4(a-A)(A-b) = (b-a)²

Answer 1

Heya.....✌

Here's ur ans. ⤵

↪ We know that arithmetic mean of a and b is a+b/2

I.e. A = a+b/2

✨ 4 - (a-A) (A-b)

= 4 - ( a - a+b/2 ) ( a+b/2 - b )

= 4 ( a - b ) ÷ 2 ( a - b ) ÷ 2

= 4 ( a-b)^2 / 4 )

= (a-b)^2

= ( b - a ) ^2
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Hope it helps

Answer 2

hello mate!.....


given........


A is the arithmatic mean of a and b. Then,

(a+b)/2=A

=> 4(a-A)(A-b)

=4{a-(a+b)/2}{(a+b)/2-b}

=4{(2a-a-b)/2}{(a+b-2b)/2}

=4{(a-b)(a-b)/4}

={-(b-a)}{-(b-a)}

=(b-a)²


hope it helps u dear........