If a3 = 335 + b3 and a = 5+b, then what is the value of a+b(given that a>0)?

Q. If a³ = 335 + b³ and a = 5+b, then what is the value of a+b(given that a>0)?

A. 7
B. 9
C. 16
D. 49

Solution: In this question, we have a³ = 335 + b³ and a = 5+b.

Let’s assume:

a³ = 335 + b³
Here we see:
a³ -b³ = 335 …..equation 1

a = 5+b
a-b = 5 ….equation 2

we know a universal formula

(a-b)³ = a³ -b³-3ab(a-b)

now we will put the value from equation 1 and equation 2 in this formulea.

(5)³ = 335-3ab(5)
125 = 335-15ab
15ab = 335-125
15ab = 210
ab =14

Let’s assume ab = 14 …equation 3

(b+5)b =14
b² +5b =14
b²+5b-14 =0

In this equation, we will use the middle term split method.

b²+7b-2b-14 =0
b(b+7)-2(b+7) =0
(b-2)(b+7)=0

So, here we get:
b=2
b=-7

Putting the value of b in equation 1

a=b+5

a=7

a = -7+5 =-2

As we know the value of a is greater then zero.

So the answer is a = 7.

If a3 = 335 + b3 and a = 5+b, then what is the value of a+b(given that a>0) From Classroom