Question

numbers are in the ratio 1: 2: 4 their product is 512 then the numbers are​

Answer 1

GiveN:-

Numbers are in the ratio 1: 2: 4 their product is 512.

To FinD:-

The numbers.

SolutioN:-

• Let the nos be x, 2x, 4x.
• Product = 512.

According to the question,

$\large\implies{\sf{x\times2x\times4x=512}}$

$\large\implies{\sf{8x^3=512}}$

$\large\implies{\sf{x^3=\dfrac{512}{8}}}$

$\large\implies{\sf{x^3=\dfrac{\cancel{512}}{\cancel{8}}}}$

$\large\implies{\sf{x^3=64}}$

$\large\implies{\sf{x=\sqrt[3]{64}}}$

$\large\therefore\boxed{\bf{x=4.}}$

The numbers are:-

• x = 4
• 2x = 2 × 4 = 8
• 4x = 4 × 4 = 16

VerificatioN:-

$\large\implies{\sf{4\times8\times16=512}}$

$\large\implies{\sf{512=512}}$

$\large\therefore\boxed{\bf{LHS=RHS.}}$

• Hence verified.

The three numbers are 4, 8 and 16.

Answer 2

x =4

• 1:2:4 = 512
• 1x × 2x × 4x = 512
• 8x³ = 512
• x³ = 64
• x= ³√64
• x = 4

1x = 1×4 = 4

1x = 1×4 = 42x = 2×4 = 8

1x = 1×4 = 42x = 2×4 = 84x = 4×4 = 16

hope it helps