Question

if a,b,c are in a.p the b^2-ac is equal to​

Answer 1

Step-by-step explanation:

$a \: b \: c \: are \: ap \: \: then \: b = \frac{a + c}{2} \\ {b}^{2} - ac = {( \frac{a + c}{2} )}^{2} - ac \\ \: \: \: \: \: \: \: \: = \frac{ {a}^{2} + {c}^{2} + 2ac }{4} - ac \\ \: \: \: \: \: \: \: \: = \frac{ {a}^{2} + {c}^{2} + 2ac - 4ac } {4} \\ \: \: \: \: \: \: \: = \frac{ {a}^{2} + {c }^{2} - 2ac }{4} \\ \: \: \: \: \: \: \: = \frac{ {(a - c)}^{2} }{4} \\ \: \: \: \: \: \: \: = {( \frac{a - c}{2}) }^{2} \\ = = = = = = = = = = = =$