If the third proportional of 2(x2 – y2) and (xy2 + x2y) is [8(x + y)

1.	If the third proportional of 2(x2 – y2) and (xy2 + x2y) is [8(x + y)/(x – y)], then find the value of xy.1). 22). 43). 84). 16
Answer» As we know, if a? B = b? c, then c is the THIRD proportional of a and b Let a = 2(X² – y²), b = (xy² + x²y), c = [8(x + y)/(x – y)] ⇒ 2(x² – y²) : (xy² + x²y) = (xy² + x²y) : [8(x + y)/(x – y)] ⇒ 2(x² – y²) × [8(x + y)/(x – y)] = (xy² + x²y) × (xy² + x²y) ? (x² – y²) = (x + y)(x – y) ⇒ 2(x + y)(x – y) × [8(x + y)/(x – y)] = xy(x + y) × xy(x + y) ⇒ 16 × (x + y)² = (xy)² × (x + y)² ⇒ 16 = (xy)² ∴ xy = √16 = 4

If the third proportional of 2(x2 – y2) and (xy2 + x2y) is [8(x + y)/(x – y)], then find the value of xy.1). 22). 43). 84). 16

Answer»

As we know, if a? B = b? c, then c is the THIRD proportional of a and b

Let a = 2(X² – y²), b = (xy² + x²y), c = [8(x + y)/(x – y)]

⇒ 2(x² – y²) : (xy² + x²y) = (xy² + x²y) : [8(x + y)/(x – y)]

⇒ 2(x² – y²) × [8(x + y)/(x – y)] = (xy² + x²y) × (xy² + x²y)

? (x² – y²) = (x + y)(x – y)

⇒ 2(x + y)(x – y) × [8(x + y)/(x – y)] = xy(x + y) × xy(x + y)

⇒ 16 × (x + y)² = (xy)² × (x + y)²

⇒ 16 = (xy)²

∴ xy = √16 = 4