Final answer:
To find the value of a:b in the equation a³ + b³ ÷ a³ - b³ = 76/49, solve for a and b. The value of a:b is 1:1.
Step-by-step explanation:
To find the value of a:b in the equation a³ + b³ ÷ a³ - b³ = 76/49, we need to solve for a and b. Let's break down the equation and solve step by step.
a³ + b³ ÷ a³ - b³ = 76/49
First, we need to simplify the expression by multiplying the denominators with the numerators:
(a³ + b³)/(a³ - b³) = 76/49
Then, we can cross-multiply:
49(a³ + b³) = 76(a³ - b³)
Now, expand the brackets:
49a³ + 49b³ = 76a³ - 76b³
Combine like terms:
125a³ = 125b³
Divide both sides by 125:
a³ = b³
Take the cube root of both sides:
a = b
So, the value of a:b is 1:1.