Question

If a,b,c are in g.p., then show that a^2,b^2,c^2 are also in g.p.

Please solve it.......

Answer 1

Step-by-step explanation:

$Given \: it \: \: a \: , \: b \: , \: c \: are \: in \: GP \: \\ then\\ {b}^{2} = ac \\ squaring \: on \: both \: sides \: , \\ {( {b}^{2} )}^{2} = {a}^{2} {c}^{2} \\ \\ Hence \: {a}^{2} \: , \: {b}^{2} \: , \: {c}^{2} are \: in \: GP \: \\ \\ \\ Hope \: it \: will \: help \: you \:$

Answer 2

$\underline\mathtt\blue{Given:}$

If a,b, c are in G.P ,then show that $\sf{ {a}^{2} , {b}^{2} ,{c}^{2} }$are also in G.P.

$\huge\underline\mathfrak\green{Solution:}$

Since, a ,b,c are in geometric progression ,

$\sf{ \frac{b}{a} = \frac{c}{b}}$

$\sf{\Implies {b}^{2} = ac}$

Now,by squaring both sides,we get,

$\sf{( {b}^{2} )^{2} = {ac}^{2} }$

Hence,a²,b²,c²are also in G.P.

[Proved]

$\rule{300}{2}$

$\huge\underline\mathfrak\red{ThankYou}$