Question

if a, b, c, d are in proportion prove that:a+b/c+d=square root(2a^2+7b^2) /squareroot(2c^2+7d^2) ​

Answer 1

Given :- a, b, c, d are in proportion .

To Proved :-

• (a + b)/(c + d) = √(2a² + 7b²) / √(2c² + 7d²)

Solution :-

since, a, b, c, d are in proportion , so,

→ a/b = c/d = Let k .

→ a = bk

→ c = dk

then, LHS :-

→ (a + b)/(c + d)

→ (bk + b) / (dk + d)

→ b(k + 1)/d(k + 1)

→ b/d

RHS :-

→ √(2a² + 7b²) / √(2c² + 7d²)

→ √(2b²k² + 7b²) / √(2d²k² + 7d²)

→ √b²(2k² + 7) / √(d²(2k² + 7)

→ √b² * √(2k² + 7) / √d² * √(2k² + 7)

→ √b²/√d²

→ b/d .

therefore,

→ LHS = RHS (Proved.)

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Answer 2

Answer:

Your answer's in the attachment fren :D