Question

please solve this . i mark this as brainliest answer​

Answer 1

Answer:

LHS = RHS

Step-by-step explanation:

$\mathrm{ Let \: \dfrac{A}{a}=\dfrac{B}{b}=\dfrac{C}{c}=\dfrac{D}{d}=k}$

So,

 A = ak  ; B = bk  ;  C = ck  ; D = dk

 Left Hand side:

⇒ √Aa + √Bb + √Cc +√Dd

⇒ √aA + √bB + √cC + √dD

     From above, values of A , B , C and D are substituted

⇒ √a( ak ) + √b( bk ) + √c( ck ) + √d( dk )

⇒ √a²k + √b²k + √c²k + √d²k

⇒ a√k + b√k + c√k + d√k

⇒ ( a + b + c + d )√k

$\implies \mathrm{\sqrt{ ( a+ b+ c + d)^2k} }\\\\\implies \mathrm{ \sqrt{(a+b+c+d)(a+b+c+d)k }}\\\\\implies \mathrm{ \sqrt{(a+b+c+d)(ak+bk+ck+dk) }}\\\\\implies \mathrm{\sqrt{(a+b+c+d)(A+B+C+D) } }$

  Hence proved LHS = RHS.