Question

Factor the polynomials completely, then solve 48x² - 75 = 0​

Answer 1

`x=(5)/(4) \text { or } x=-(5)/(4)`

Explanation:

48 = 3 × 16

75 = 3 × 25

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Then, a Complete factorization of 48x² - 75 is :

`\begin{aligned}48 x^(2)-75 &=3 *\left(16 x^(2)\right)-3 *(25) \\&=3 *\left(16 x^(2)-25\right)\end{aligned}`

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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

`\begin{array}{l}16 x^(2)-25=0 \\\\\Leftrightarrow 16 x^(2)=25 \\\\\Leftrightarrow x^(2)=(25)/(16) \\\\\Leftrightarrow x=\sqrt{(25)/(16)} \text { or } x=-\sqrt{(25)/(16)} \\\\\Leftrightarrow x=(5)/(4) \text { or } x=-(5)/(4)\end{array}`