Home
Class 10
MATHS
If a/b = c/d = e/f, prove that (b^2 + ...

If `a/b = c/d = e/f`, prove that `(b^2 + d^2 + f^2)(a^2 + c^2 + e^2) = (ab + cd + ef)^2`

Text Solution

Verified by Experts

`a/b=c/d=e/f=k`
`a/b=k,c/d=k,e/f=k`
`a=kb,c=kd,e=kf`
LHS
`=(b^2+d^2+f^2)(a^2+c^2+e^2)`
`=(b^2+d^2+f^2)(k^2b^2+k^2d^2+k^2f^2)`
`=k^2(b^2+d^2+f^2)^2`
RHS
...
Promotional Banner

Similar Questions

Explore conceptually related problems

If a/b = b/c = c/d , then prove that (a^(2) + b^(2) + c^(2))(b^(2) + c^(2)+d^(2)) = (ab + bc cd)^(2)

If a : b = c : d = e : f , then prove that (a^(2) + c^(2) + e^(2)) (b^(2)+d^(2)+f^(2)) = (ab + cd + ef)^(2))

If a/b = c/d =e/f = 4, then (m ^(2) a + n^(2) c + p ^(2) e )/( m ^(2) b + n ^(2) d + p ^(2) f )=?

If a/b = c/d = e/f , then prove that each of these ratio's is equal to ((4a^(2)+3c^(2)-7e^(2))/(4b^(2)+3d^(2)-7f^(2)))^(1//2)

If a : b = c : d , then prove that the - proportional of (a^(2) + c^(2)) " and " (b^(2) + d^(2)) " is " (ab + cd) .

If a/b=c/d=e/f=9/5 then (2a + 3c + 5e)/( 2b + 3d + 5f) = ?

If a+c = 2b and 2/c= 1/b+1/d then prove that a:b = c:d.