Question

Three numbers are in the ratio 1 : 2 : 3 and the sum of their cubes is 288. Find the numbers.

Answer 1

Answer:

let the no. be x,2x and 3x

sum of their cubes is 36x^3

x^3=8

x=2

the nos . are 2,4,6

Answer 2

$\sf Let \: the \: ratio \: be \: x. \\ \: \: \: \: \: \: \sf \bullet \: 1st \: number = 1x \\ \: \: \: \: \: \: \sf \bullet \:2nd \: number = 2x \\ \: \: \: \: \: \: \sf \bullet \:3rd \: number = 3x$

$\\ \bf \underline{Given} \\ \sf \to\: Sum \: of \: their \: cubes = 288$

$\sf \implies(1x) {}^{3} + (2x) {}^{3} + (3x) {}^{3} = 288 \\ \sf \implies \: 1x {}^{3} + 8x {}^{3} + 27x {}^{3} = 288 \\ \sf \implies \: x {}^{3} (1 +8 + 27) = 288 \\ \sf \implies \: x {}^{3} (36) = 288 \\ \sf \implies \: x {}^{3} = \dfrac{288}{36}$

$\small \implies \boxed {\boxed {\tt \blue { x = 2}}}$

$\\ \therefore \sf\underline{Numbers \: will \: be} : \\ \: \: \: \: \: \: \: \: \bullet \: 1x \to \: 1( 2 ) \to \: 2 \\ \: \: \: \: \: \: \: \: \bullet \:2x \to \: 2( 2 ) \to \: 4 \\ \: \: \: \: \: \: \: \: \bullet \:3x \to \: 3( 2 ) \to 6$