Solve the following equation by factorisation:
x215−x3−10=0.\dfrac{x^2}{15} - \dfrac{x}{3} -10 = 0.15x2−3x−10=0.
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Given,
x215−x3−10=0⇒x2−x×5−10×1515=0⇒x2−5x−150=0⇒x2−15x+10x−150=0⇒x(x−15)+10(x−15)=0⇒(x+10)(x−15)=0 (Factorising left side) ⇒x+10=0 or x−15=0 (Zero-product rule) x=−10 or x=15\dfrac{x^2}{15} - \dfrac{x}{3} -10 = 0 \\[1em] \Rightarrow \dfrac{x^2 - x \times 5 - 10 \times 15}{15} = 0 \\[1em] \Rightarrow x^2 - 5x - 150 = 0 \\[1em] \Rightarrow x^2 - 15x + 10x - 150 = 0 \\[1em] \Rightarrow x(x - 15) + 10(x - 15) = 0 \\[1em] \Rightarrow (x + 10)(x - 15) = 0 \text{ (Factorising left side) } \\[1em] \Rightarrow x + 10 = 0 \text{ or } x - 15 = 0 \text{ (Zero-product rule) } \\[1em] x = -10 \text{ or } x = 15 \\[1em]15x2−3x−10=0⇒15x2−x×5−10×15=0⇒x2−5x−150=0⇒x2−15x+10x−150=0⇒x(x−15)+10(x−15)=0⇒(x+10)(x−15)=0 (Factorising left side) ⇒x+10=0 or x−15=0 (Zero-product rule) x=−10 or x=15
Hence, the roots of given equation are -10 , 15.
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x+1x=2120x + \dfrac{1}{x} = 2\dfrac{1}{20}x+x1=2201
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