Question

If a upon b is equal to c upon d is equal to e upon f then value of 2a square + 3 c square plus 4 e square upon 2 b square + 3 d square + 4 f square is equal to

Answer 1

$\therefore \frac{2a^2+3c^2+4e^2}{2b^2+3d^2+2f^2}=(\frac ab)^2=(\frac cd)^2=(\frac ef)^2$

Step-by-step explanation:

Given that,

$\frac ab=\frac cd=\frac ef =r(say)$

Then,          

$\frac ab=r$

⇒a=br

Similarly,

c= dr and e= fr

We need to find out the value of

$\frac{2a^2+3c^2+4e^2}{2b^2+3d^2+2f^2}$

Now putting the value of a,c and d

$=\frac{2(br)^2+3(dr)^2+4(fr)^2}{2b^2+3d^2+2f^2}$

$=\frac{2b^2r^2+3d^2r^2+4f^2r^2}{2b^2+3d^2+2f^2}$

$=\frac{r^2(2b^2+3d^2+4f^2)}{2b^2+3d^2+2f^2}$   [taking common r² from the denominator]

$=r^2$                      [ cancel (2b²+3d²+4f²)]

$=(\frac ab)^2$                   $[\because \frac ab =r]$

$=(\frac cd)^2$                   $[\because \frac cd=r]$

$=(\frac ef)^2$                   $[\because \frac ef=r]$

$\therefore \frac{2a^2+3c^2+4e^2}{2b^2+3d^2+2f^2}=(\frac ab)^2=(\frac cd)^2=(\frac ef)^2$

Answer 2

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Step-by-step explanation:

No idea

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