Question

2.
If
a3 + b3
a3-b3
76/49
find the value of a : b.

Answer 1

Answer: 5:3

Step-by-step explanation:

Given (a^3 + b^3)/(a^3-b^3) =76/49

Applying componendo and dividendo which states that if a/b=c/d, then (a+b)/(a-b) = (c+d)/(c-d),

we get (a^3+b^3 +a^3-b^3)/(a^3+b^3-a^3+b^3) = (76+49)/(76–49)

which gives us 2a^3/2b^3 = 125/27

or a^3/b^3 = 125/27

So a:b = 5:3.

Answer 2

Answer:

a3+b3/a3−b3=76/49a3+b3/a3−b3=76/49

implies, 49a3+49b3=76a3−76b349a3+49b3=76a3−76b3 [by cross multiplying]

implies, 125b3=27a3125b3=27a3[taking all the a3a3in one side and b3b3 in another side]

implies , a3/b3=125/27a3/b3=125/27

implies that (a/b)3=(5/3)3(a/b)3=(5/3)3

Applying cube root on both sides , we get,

a/b=5/3a/b=5/3thereforea:b=5:3a:b=5:3