if arithmetic and geometric mean of x and y is 8 and 3√7, respectively, then the value of x³+ y³is :

Question

Question

This question was previously asked in

SSC Graduation Level Previous Paper (Held on: 1 Aug 2022 Shift 4)

Answer 1

Given:

Arithmetic means (A.M) = 8

Geometric means(G.M) = 3√7

Formula Used:

A.M = (a + b)/2

G.M = √(ab)

x³ + y³ = ( x + y )³ - 3xy(x + y)

Calculations:

According to the questions,

⇒ A.M = (x + y)/2

⇒ 8 = (x + y)/2

⇒ x + y = 16

⇒ G.M = √(xy)

⇒ 3√7 = √(xy)

On squaring both sides, we get

⇒ 9 × 7 = xy

⇒ xy = 63

Now,

⇒ x3 + y3 = (x + y)3 - 3xy(x + y) = (16)3 - 3 × 63 × 16 = 4096 - 3024 = 1072

Hence, the value of x³ + y³ is 1072

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