Question

16x² + y² = 48, xy = 2, then 64x³ + y³ =?
solve it​

Answer 1

➠ Given :

⟼ 16x² + y² =48

⟼ xy = 2

➠ To Find :

64x³+y³

➠ Solution :

⟹ 16x² + y² = 48

⟹ (4x)² + y² = 48

⟹ (4x)² + y² + 8xy = 48 + 8xy [∵ xy = 2]

⟹ (4x+y)² = 48 + 16

⟹ (4x+y)² = 64

⟹ (4x+y)² = (8)²

∴ 4x+y = 8

By applying (a+b)³ = a³+b³+3(ab)(a+b)

⟹ (4x+y)³ = 8³

⟹ 64x³+y³+3(4xy)(4x+y) = 512

⟹ 64x³+y³+(3×8×8) = 512

⟹ 64x³+y³+ 192 = 512

⟹ 64x³+y³ = 512-192

∴ 64x³+y³ = 320

Answer 2

We know that;

Given data:

16x² + y² =48

 xy = 2

Find out:

64x³+y³

Let us:

the given data is 16x² + y² = 48

so,

 (4x)² + y² = 48

(4x)² + y² + 8xy = 48 + 8xy [∵ xy = 2]

(4x+y)² = 48 + 16

(4x+y)² = 64

(4x+y)² = (8)²

∴ 4x+y = 8

Now by applying

(a+b)³ = a³+b³+3(ab)(a+b)

(4x+y)³ = 8³

64x³+y³+3(4xy)(4x+y) = 512

64x³+y³+(3×8×8) = 512

64x³+y³+ 192 = 512

64x³+y³ = 512-192

             = 320

Hence  64x³ + y³ = 320