Question

$if \: (a + b + c)(a - b + c ) = {a}^{2} + {b}^{2} + {c}^{2} .then \: sow \: that \: a \: b \: c \: are \: in \: continued \: proportion$
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Answer 1

solutio :-

answer :

$(a + b + c)(a - b + c) = {a}^{2} + {b}^{2} + {c}^{2}$

$a(a - b + c) + b(a - b + c) + c(a - b + c) = {a}^{2} + {b}^{2} + {c}^{2}$

$ac + ac - {b}^{2} = {b}^{2}$

$2ac = {b}^{2} + {b}^{2}$

$2ac = 2 {b }^{2}$

$ac = {b}^{2}$

Therefore :

a , b , c is in continued proportion.

Answer 2

Answer:

(a+b+c)(a-b+c)=a2+b2+c2

⇒

(a+c)2-b2=a2+b2+c2

⇒

a2+c2+2ac-b2=a2+b2+c2

⇒

2b2=2ac

⇒

b2=ac

Therefore, a, b, c are in continued proportion.

Explanation:

(a+b+c)(a−b+c)=a

2

+b

2

+c

2

.thensowthatabcareincontinuedproportion