Answer:
[tex]x=\frac{5}{4} \text { or } x=-\frac{5}{4}[/tex]
Step-by-step explanation:
48 = 3 × 16
75 = 3 × 25
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Then, a Complete factorization of 48x² - 75 is :
[tex]\begin{aligned}48 x^{2}-75 &=3 \times\left(16 x^{2}\right)-3 \times(25) \\&=3 \times\left(16 x^{2}-25\right)\end{aligned}[/tex]
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Now let’s solve our equation 48x² - 75 = 0
48x² - 75 = 0 means 3 × (16x² − 25) = 0 means 16x² − 25 = 0
[tex]\begin{array}{l}16 x^{2}-25=0 \\\\\Leftrightarrow 16 x^{2}=25 \\\\\Leftrightarrow x^{2}=\frac{25}{16} \\\\\Leftrightarrow x=\sqrt{\frac{25}{16}} \text { or } x=-\sqrt{\frac{25}{16}} \\\\\Leftrightarrow x=\frac{5}{4} \text { or } x=-\frac{5}{4}\end{array}[/tex]
