āϝāĻĻāĻŋ $x=\sqrt{2+\sqrt{2+\sqrt{2+….}}}$ āĻšāϞ⧠x āĻāϰ āĻŽāĻžāύ āĻāϤ?
(a) 2,-1 (b) -2,1 (c) 3,2 (d) 2,5
āϝāĻĻāĻŋ $x=\sqrt{2+\sqrt{2+\sqrt{2+….}}}$ āĻšāϞ⧠x āĻāϰ āĻŽāĻžāύ āĻāϤ? (a) 2,-1 (b) -2,1 (c) 3,2 (d) 2,5
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āϧāϰāĻŋ $x=\sqrt{2+\sqrt{2+\sqrt{2+….\propto }}}$
āĻ āϰā§āĻĨāĻžā§, $\sqrt{2+x}=\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+….\propto }}}}$
āĻŦāĻž , $\sqrt{2+x}=x$
āĻŦāĻž, ${{\left( \sqrt{2+x} \right)}^{2}}={{x}^{2}}$
āĻŦāĻž, $2+x={{x}^{2}}$
āĻŦāĻž, $-{{x}^{2}}+2+x=0$
āĻŦāĻž, ${{x}^{2}}-x-2=0$
āĻŦāĻž, ${{x}^{2}}-2x+x-2=0$
āĻŦāĻž, $x(x-2)+1(x-2)=0$
āĻŦāĻž, $(x-2)(x+1)=0$
āĻ āϰā§āĻĨāĻžā§ $(x-2)=0$ āĻāĻŋāĻāĻŦāĻž $(x+1)=0$ āĻāĻŋāĻāĻŦāĻž āĻāĻā§ā§āϰ āĻŽāĻžāύ = 0
āĻ āϤāĻāĻŦ , $(x-2)=0$ āĻšāϞ⧠, x=2 āĻāĻŦāĻ $(x+1)=0$ āĻšāϞ⧠, x=-1
āĻāϤā§āϤāϰāĻ x āĻāϰ āĻŽāĻžāύ (a) 2 , -1