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

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