Question

If a:b = c:d then prove that 1/ma+1/nb+1/pc +1/qd =[a/q+b/p+c/n+d/m]×1/(abcd)^1/2

pls answer it fast

Answer 1

Answer:

Answer by Method 1 ::

a: b - c: d multiply RHS with m/m and LHS with n/n then we will get

ma / mb = nc / nd or ma / nc = mb / nd

add 1 both sides then (ma / nc ) + 1 = (mb / nd ) + 1

(ma + nc ) / nc = ( mb + nd ) / nd or

(ma + nc ) / ( mb + nd ) = nc / nd = c/d

Hence (ma + nc ) : ( mb + nd ) = c : d

Answer by Method 2 ::

a: b - c: d multiply RHS with m/m and LHS with n/n then we will get

ma / mb = nc / nd or ma / nc = mb / nd

Apply COMPONENDO Rule now i.e., if a/d = c/d then (a+b)/b = (c+d)/ d

(ma + nc ) / nc = ( mb + nd ) / nd or

(ma + nc ) / ( mb + nd ) = nc / nd = c/d

Hence (ma + nc ) : ( mb + nd ) = c : d

Answer 2

Explanation:

such a simple question, but seems tricky......