Question

three numbers r in the ratio 1:2:3 the sum of their cube is 98784 find the no.​

Answer 1

SOLUTION:

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QUESTION:

Three numbers are in the ratio 1:2:3 the sum of their cube is 98784 find the no.?

ANSWER:

The numbers are = 14 , 28 , 42.

GIVEN:

Three numbers are in the ratio = 1:2:3

The sum of their cube = 98784

TO FIND:

Find the numbers?

SOLUTION:

Let the three numbers be x , 2x , 3x

according to the question,

(x)³ + (2x)³ + (3x)³ = 98784

x³ + 8x³ + 27x³ = 98784

36x³ = 98784

x³ = 98784/36

x³ = 2744

$x = 3\sqrt{2744}$

x = 14.

Hence , x = 14 , 2x = 2×14 = 28 , 3x = 3×14 = 42

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Answer 2

${\huge{\underbrace{\rm{Question:-}}}}$

Q) Three numbers are in the ratio 1:2:3 , if the sum of their cubes is 98784 , find the numbers.

${\huge{\rm{\underbrace{Answer\;\checkmark}}}}$

$\frak{Given}\begin{cases}\sf{Ratio\;of\;the\;numbers=\bf{1:2:3}}\\ \sf{Sum\;of\;their\;cubes=\bf{98784}}\end{cases}$

★ To Find : The numbers.

★ Solution :-

Let the ratios be 1x , 2x & 3x

It means

• First number = 1x
• Second number = 2x
• Third number = 3x .

${\textit{\textbf{According\;to \;the\;Question:}}}$

$\mapsto \rm \: {(1x)}^{3} + {(2x)}^{3} + {(3x)}^{3} = 98784 \\ \\ \mapsto \rm \: {x}^{3} + 8 {x}^{3} + 27 {x}^{3} = 98784 \\ \\ \mapsto \rm \: \cancel{36 }{x}^{3} = \cancel{98784}$

$\\ \mapsto \rm \: {x}^{3} = 2744 \\ \\ \mapsto \rm \: x = \sqrt[3]{2744} \\ \\ \mapsto \: \underline{ \boxed{ \sf{x = 14}}}$

So ,

$\bull \sf \: first \: no. = x = \bf14$

$\bull \sf \: second \: no. = 2x = 2 \times 14 = \bf{28}$

$\bull \sf \: third \: no. = 3x = 3 \times 14 = \bf42$