Question

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

Answer 1

Answer:

$\huge\pink{\boxed{\blue{\boxed{ \purple{ \boxed{{\pink{Answer}}}}}}}} \\ \large\pink{\boxed{\blue{\boxed{ \purple{ \boxed{{\pink{Your~answer↓}}}}}}}} \\ \small\bold\red{question \: from \: sequence \: and \: series} \\ Since, \: A \: is \: the \: A.M. \: between \: a \: and \: b, \\ </p><p>so \: A = \: \frac{a + b}{2} \\ </p><p>Consider \: 4 (a - A)(A - b) \\ = 4(a - \frac{a + b}{2} )( \frac{a + b}{2} - b) \\ = 4( \frac{2a - a - b}{2} )( \frac{a + b - 2b}{2} ) \\ = (a - b)(a - b) \\ = (b - a)(b - a) \\ = {(b - a)}^{2}$

Answer 2

Step-by-step explanation:

At last it is

${a - b }^{2}$