Question

three numbers are in ratio 1:2:4 their produce 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

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}}⟹x×2x×4x=512

\large\implies{\sf{8x^3=512}}⟹8x

3

=512

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

3

=

8

512

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

3

=

8

512

\large\implies{\sf{x^3=64}}⟹x

3

=64

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

3

64

\large\therefore\boxed{\bf{x=4.}}∴

x=4.

The numbers are:-

x = 4

2x = 2 × 4 = 8

4x = 4 × 4 = 16

VerificatioN:-

\large\implies{\sf{4\times8\times16=512}}⟹4×8×16=512

\large\implies{\sf{512=512}}⟹512=512

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

LHS=RHS.

Hence verified.

The three numbers are 4, 8 and 16.