Question

The positive solution to the equation x^2- 4 = 6

Answer 1

Answer:

In the form of $a+\sqrt{b}$,

• a = 3
• b = 13

Explanation:

The equation can be rewritten as:

$x^{2} -6x-4=0$

Find the solutions using the quadratic formula:

• a = 1
• b = -6
• c = -4

$x=\frac{-b+-\sqrt{b^{2}-4ac} }{2a} \\\\=\frac{-(-6)+-\sqrt{(-6)^{2} -4(1)(-4)} }{2(1)} \\\\=\frac{6+-\sqrt{36+16} }{2} \\\\=\frac{6+-\sqrt{52} }{2} \\\\=\frac{2(3)+-2\sqrt{13} }{2} \\\\=\left \{ {{x_{1}=3+\sqrt{13} } \atop {x_{2}=3-\sqrt{13} }} \right.$

Find the solution that's positive:

$\left \{ {{x_{1} = 3+\sqrt{13} = 6.605551275... } \atop {x_{2} = 3-\sqrt{13} = -0.605551275... }} \right$

Therefore, the solution would be $3+\sqrt{13}$.

In the form of $a+\sqrt{b}$,

• a = 3
• b = 13