Question

the three numbers are in ratio as 2:3:4 .if the sum of their cubes is 50688 find the numbers.​

Answer 1

Answer:

Let the numbers a,b & c

now, a:b:c=2:3:4

So,

2

a

=

3

b

=

4

c

let,

2

a

=

3

b

=

4

c

=k,k∈R

a=2k,b=3k &c=4k,k∈R

now, given that a

3

+b

3

+c

3

=50688

∴(2k)

3

+(3k)

3

+(4k)

3

=50688

∴8k

3

+27k

3

+64k

3

=50688

∴99k

3

=50688

k

3

=

99

50688

k

3

=512

k=(512)

1/3

k=8

So, a=2(k)=2(8)=16

b=3(k)=3(8)=24

c=4(k)=4(8)=32

Answer 2

ANSWER

Let the numbers a,b & c

now, a:b:c=2:3:4

So, 2a

= 3b

=4c

let,

2a=3b=4c

=k,k∈R

a=2k,b=3k &c=4k,k∈R

now, given that a3

+b3

+c3

=50688

∴(2k)3

+(3k)3

+(4k)3

=50688

∴8k3

+27k3

+64k3

=50688

∴99k3

=50688

k3=99

50688

k3=512

k=(512)

1/3

k=8

So, a=2(k)=2(8)=16

b=3(k)=3(8)=24

c=4(k)=4(8)=32

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