Q. If a^{3} = 335 + b^{3} 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 a^{3} = 335 + b^{3} and a = 5+b.

Let’s assume:

a^{3} = 335 + b^{3}

Here we see:

a^{3} -b^{3} = 335 …..equation 1

a = 5+b

a-b = 5 ….equation 2

we know a universal formula

(a-b)^{3} = a^{3} -b^{3}-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

b^{2} +5b =14

b^{2}+5b-14 =0

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

b^{2}+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

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