Question

Find the solutions of the following equations by extracting square roots 9x2-16=0 (z-2)2-36=0

Answer 1

The solutions of the equation $9x$² - 16 = 0is 4/3 and -4/3 and that of the equation $(z - 2)^{2} - 36 = 0$ is 8 and -4.

Solving the both quadratic equations by extracting square roots:

$9x^{2} - 16 = 0$

⇒ $9x^{2} = 16$                                    

∴ On taking square-root of both sides, we get

$\sqrt{9x^{2} }$ = $\sqrt{16}$

⇒ $3x =$ $+4$ and $3x = -4$

⇒ $x$ = 4/3 and $x$ = -4/3

For the equation, $(z - 2)^{2} - 36 = 0$, the solution is:

$(z - 2)^{2} - 36 = 0$

⇒ $(z - 2)^{2} = 36$

∴ On taking square-root of both sides, we get

$\sqrt{(z - 2)^{2} } = \sqrt{36}$

⇒ (z - 2) = 6 and (z - 2) = -6

⇒ z = 6 +2 and z = -6 + 2

⇒ z = 8 and z = -4

The solution of the equation $9x^{2} - 16 = 0$ is 4/3 and -4/3.

The solution of the equation $(z - 2)^{2} - 36 = 0$ is 8 and -4.

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