The solutions of the equation [tex]9x[/tex]² - 16 = 0is 4/3 and -4/3 and that of the equation [tex](z - 2)^{2} - 36 = 0[/tex] is 8 and -4.
Solving the both quadratic equations by extracting square roots:
[tex]9x^{2} - 16 = 0[/tex]
⇒ [tex]9x^{2} = 16[/tex]
∴ On taking square-root of both sides, we get
[tex]\sqrt{9x^{2} }[/tex] = [tex]\sqrt{16}[/tex]
⇒ [tex]3x =[/tex] [tex]+4[/tex] and [tex]3x = -4[/tex]
⇒ [tex]x[/tex] = 4/3 and [tex]x[/tex] = -4/3
For the equation, [tex](z - 2)^{2} - 36 = 0[/tex], the solution is:
[tex](z - 2)^{2} - 36 = 0[/tex]
⇒ [tex](z - 2)^{2} = 36[/tex]
∴ On taking square-root of both sides, we get
[tex]\sqrt{(z - 2)^{2} } = \sqrt{36}[/tex]
⇒ (z - 2) = 6 and (z - 2) = -6
⇒ z = 6 +2 and z = -6 + 2
⇒ z = 8 and z = -4
The solution of the equation [tex]9x^{2} - 16 = 0[/tex] is 4/3 and -4/3.
The solution of the equation [tex](z - 2)^{2} - 36 = 0[/tex] is 8 and -4.
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