Question

Using properties of proportion, solve for X: (x^3 + 27x)÷(9x^2+27)=63÷62​

Answer 1

Simplify ——

62

Equation at the end of step

1

:

x 63

(((x3)+((27•—)•(x2)))+27)-—— = 0

9 62

STEP

2

:

x

Simplify —

9

Equation at the end of step

2

:

x 63

(((x3)+((27•—)•x2))+27)-—— = 0

9 62

STEP

3

:

Multiplying exponential expressions :

3.1 x1 multiplied by x2 = x(1 + 2) = x3

Equation at the end of step

3

:

63

(((x3) + 3x3) + 27) - —— = 0

62

STEP

4

:

Rewriting the whole as an Equivalent Fraction

4.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using 62 as the denominator :

4x3 + 27 (4x3 + 27) • 62

4x3 + 27 = ———————— = ———————————————

1 62

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Trying to factor as a Sum of Cubes:

4.2 Factoring: 4x3 + 27

Theory : A sum of two perfect cubes, a3 + b3 can be factored into :

(a+b) • (a2-ab+b2)

Proof : (a+b) • (a2-ab+b2) =

a3-a2b+ab2+ba2-b2a+b3 =

a3+(a2b-ba2)+(ab2-b2a)+b3=

a3+0+0+b3=

a3+b3

Check : 4 is not a cube !!

Answer 2

Using properties of proportion, solve for X: (x^3 + 27x)÷(9x^2+27)=63÷62

Anwer a= 9/2