Question

If (a+b+c) (a-b+c)=a²+b²+c2 show that a, b, c are in continued proportion.

Answer 1

Step-by-step explanation:

in this question we have to prove that

$\frac{a}{b }= \frac{b}{c} \\ \\ let \: a = 1 \\ b = 2 \\ then \: c = 4 \\ which \: satisfy \: the \: proportion \\ \\ now \: put \: these \: values \: \\ in \: given \: question \: \\ \\lhs = (a + b + c)(a - b + c) \\ \: \: \: \: \: \: \: \: = (1 + 2 + 4)(1 - 2 + 4) \\ \: \: \: \: \: \: \: \: = 7 \times 3 \\ \: \: \: \: \: \: \: \: = 21 \\ \\ rhs = {a}^{2} + {b}^{2} + {c}^{2} \\ = 1 + {2}^{2} + {4}^{2} \\ = 21 \\ \\ lhs = rhs \\ prooved \: \:$