If a-b-c are A-P prove that-a-c-2-4-b-2-ac-

Question

Toppr Admin · Accepted Answer

RHS -4b2-x2212-4ac-xA0- -xA0- -4-a-c2-2-x2212-4ac-xA0- -xA0- -44-a2-c2-2ac-x2212-4ac-xA0- -xA0- -a2-c2-x2212-2ac-xA0- -xA0- -a-x2212-c-2-xA0- -xA0- -LHS

If $a, b, c$ are A.P prove that:
${(a - c)}^{2} = 4 (b^{2} - a c)$

RHS $= 4 b^{2} - 4 a c$
$= 4 {(\frac{a + c}{2})}^{2} - 4 a c$
$= \frac{4}{4} (a^{2} + c^{2} + 2 a c) - 4 a c$
$= a^{2} + c^{2} - 2 a c$
$= (a - c)^{2}$
$= L H S$

If a,b,c are A.P prove that:(a−c)2=4(b2−ac)

RHS =4b2−4ac =4(a+c2)2−4ac =44(a2+c2+2ac)−4ac =a2+c2−2ac =(a−c)2 =LHS

If $a, b, c$ are A.P prove that:
${(a - c)}^{2} = 4 (b^{2} - a c)$

RHS $= 4 b^{2} - 4 a c$
$= 4 {(\frac{a + c}{2})}^{2} - 4 a c$
$= \frac{4}{4} (a^{2} + c^{2} + 2 a c) - 4 a c$
$= a^{2} + c^{2} - 2 a c$
$= (a - c)^{2}$
$= L H S$