Mathematics Question and Solution
m⁶(m³+1) = 36
Let p = m³
Therefore;
m⁶ = m³*m³ = p*p = p²
It implies;
p²(p+1) = 36
p³+p² = 36
Using Substitution Approach (Substituting prime factor of 36 only in the equation 'p³+p² = 36' to get p).
The prime factors of 36 = 2 and 3.
For p = 2
Therefore;
2³+2² ≠ 36 but 12, p ≠ 2
For p = 3
Therefore;
3³+3² = 36
It implies;
p = 3
And
p = m³
Therefore;
m³ = 3
m = (3)^(⅓)
Or
m = crt(3)
Checking accuracy.
((crt(3)))⁹+((crt(3)))⁶
= (3)^(9/3)+(3)^(6/3)
= 3³+3²
= 27+9
= 36
