# At present suman's age is 7 more than a cube number and 12 less than its immediate next cube number.in how many years will suman be 40 years?

2
by ekalavyaachanta

2015-04-26T17:51:51+05:30

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Let Suman's age = x and the number = y
So, x = 7 + y³
And the next no. to y = y + 1
So, x = 7 + y³ = (y + 1)³ - 12
So,
7 + y³ = (y + 1)³ -12
7 + y³ = y³ +1³ +3(y² × 1) + 3(y × 1²) -12 {Using identity: (a + b)³ = a³ + b³ + 3a²b + 3ab²}

7 + y³ = y³ + 1 + 3y² + 3y -12
7 +12 -1 = y³ - y³ + 3y² + 3y
18 = 3(y² + y)
6 = y² +y
y² + y - 6 = 0
y² + 3y - 2y - 6 = 0
y(y + 3) - 2(y + 3) = 0
(y - 2)(y + 3) = 0
Since, we want a positive number for prefering age,
y - 2 = 0
y = 2
So,
x = (2)³ +7 = 8 + 7 = 15
So, 40-15 = 25 more years will be needed for suman to become 40 years old.
2015-04-26T21:20:54+05:30

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Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Suman's age  S = 7 + N³      ,   let N be a positive integer
S = (N+1)³ - 12

So   N³ + 7 = N³ + 3 N² + 3 N + 1  - 12

=>  3 N² + 3 N - 18 = 0
=>    N² + N - 6 = 0 ,                   -6 factors = 3 & -2  whose sum is +1.
=>    (N - 2 ) (N + 3) = 0
N = 2  or - 3  , we ignore the negative value.

Suman's age = 7 + 2³ = 15 yrs
Sumans' age will be 40 years after 25 years