Solve the following equations by factorisation:
3x2+10x+73\sqrt{3}x^2 + 10x + 7\sqrt{3}3x2+10x+73 = 0
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Given,
⇒3x2+10x+73=0⇒3x2+7x+3x+73=0⇒x(3x+7)+3(3x+7)=0⇒(x+3)(3x+7)=0⇒x+3=0 or 3x+7=0⇒x=−3 or x=−73⇒x=−3 or x=−7×33×3⇒x=−3 or x=−733\Rightarrow \sqrt{3}x^2 + 10x + 7\sqrt{3} = 0 \\[1em] \Rightarrow \sqrt{3}x^2 + 7x + 3x + 7\sqrt{3} = 0 \\[1em] \Rightarrow x(\sqrt{3}x + 7) + \sqrt{3}(\sqrt{3}x + 7) = 0 \\[1em] \Rightarrow (x + \sqrt{3})(\sqrt{3}x + 7) = 0 \\[1em] \Rightarrow x + \sqrt{3} = 0 \text{ or } \sqrt{3}x + 7 = 0 \\[1em] \Rightarrow x = -\sqrt{3} \text{ or } x = -\dfrac{7}{\sqrt{3}} \\[1em] \Rightarrow x = -\sqrt{3} \text{ or } x = -\dfrac{7 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}} \\[1em] \Rightarrow x = -\sqrt{3} \text{ or } x = - \dfrac{7\sqrt{3}}{3}⇒3x2+10x+73=0⇒3x2+7x+3x+73=0⇒x(3x+7)+3(3x+7)=0⇒(x+3)(3x+7)=0⇒x+3=0 or 3x+7=0⇒x=−3 or x=−37⇒x=−3 or x=−3×37×3⇒x=−3 or x=−373
Hence, roots of given equation are −3,−733-\sqrt{3}, -\dfrac{7\sqrt{3}}{3}−3,−373.
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3x2 + 11x + 10 = 0
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6x−2x−1=1x−2\dfrac{6}{x} - \dfrac{2}{x - 1} = \dfrac{1}{x - 2}x6−x−12=x−21
