How to solve X cubed plus X squared=12?

Answer 1

To solve the equation X^3 + X^2 = 12, you'll need to find the values of X that satisfy the equation. Here's how you can solve it:

Rewrite the equation in standard form, setting it equal to zero:

X^3 + X^2 - 12 = 0

This equation is a cubic equation. To solve it, you can try factoring it or use numerical methods such as the Newton-Raphson method. In this case, factoring is a suitable method.

First, look for common factors that can be factored out from all the terms. In this case, you can factor out X^2:

X^2(X + 1) - 12 = 0

Now, you have a quadratic equation in the form (X^2 - 12)(X + 1) = 0. This equation can be factored further:

(X - √12)(X + √12)(X + 1) = 0

You now have three factors:

a) X - √12 = 0

b) X + √12 = 0

c) X + 1 = 0

Solve each of these equations for X:

a) X - √12 = 0

X = √12

b) X + √12 = 0

X = -√12

c) X + 1 = 0

X = -1

So, the solutions for X in the equation X^3 + X^2 = 12 are X = √12, X = -√12, and X = -1.

Answer 2

By 'Trial and error'.

x^3 + x^2 = 12

Try '1'

1^3 + 1^2 = 1 + 1 = 2 Not equal to '12'

Try '2'

2^3 + 2^2 = 8 + 4 = 12 The answer

Hence the value of 'x' is '2'.