Determine if 3 is a Root of the Equation Question: Determine if \(3\) is a root of the equation: \[ \sqrt{x^2-4x+3}+\sqrt{x^2-9} = \sqrt{4x^2-14x+16} \] Solution To check whether \(3\) is a root, substitute \(x=3\) into the equation. Left-Hand Side (LHS) \[ \sqrt{3^2-4(3)+3}+\sqrt{3^2-9} \] \[ =\sqrt{9-12+3}+\sqrt{9-9} \] \[ =\sqrt{0}+\sqrt{0} \] \[ =0+0 \] \[ =0 \] […]
Find the Value of k for which the Given Value is a Solution Question: Find the value of \(k\) for which the given value is a solution of the equation: \[ x^2+3ax+k=0 \] Given, \[ x=-a \] Solution Since \(x=-a\) is a solution, it must satisfy the given equation. Substituting \(x=-a\) into the equation: \[
Find the Value of k for which the Given Value is a Solution Question: Find the value of \(k\) for which the given value is a solution of the equation: \[ kx^2+\sqrt2\,x-4=0 \] Given, \[ x=\sqrt2 \] Solution Since \(x=\sqrt2\) is a solution, it must satisfy the equation. Substituting \(x=\sqrt2\) into the equation: \[ k(\sqrt2)^2+\sqrt2(\sqrt2)-4=0
Find the Value of k for which the Given Value is a Solution Question: Find the value of \(k\) for which the given value is a solution of the equation: \[ x^2-x(a+b)+k=0 \] Given, \[ x=a \] Solution Since \(x=a\) is a solution, it must satisfy the given equation. Substituting \(x=a\) into the equation: \[
Find the Value of k for which the Given Value is a Solution Question: Find the value of \(k\) for which the given value is a solution of the equation: \[ 7x^2+kx-3=0 \] Given, \[ x=\frac{2}{3} \] Solution Since \(x=\frac{2}{3}\) is a solution, it must satisfy the equation. Substituting \(x=\frac{2}{3}\) into \[ 7x^2+kx-3=0, \] we
Determine Whether the Given Values Are Solutions of the Equation Question: Determine whether the given values are solution of the given equation or not: \[ a^2x^2-3abx+2b^2=0 \] (i) \(x=\frac{a}{b}\) (ii) \(x=\frac{b}{a}\) Solution A value of \(x\) is a solution if it makes the left-hand side equal to zero. Checking \(x=\frac{a}{b}\) Substitute \(x=\frac{a}{b}\): \[ a^2\left(\frac{a}{b}\right)^2-3ab\left(\frac{a}{b}\right)+2b^2 \]
Determine Whether the Given Values Are Solutions of the Equation Question: Determine whether the given values are solution of the given equation or not: \[ x^2-\sqrt2\,x-4=0 \] (i) \(x=-\sqrt2\) (ii) \(x=-2\sqrt2\) Solution A value of \(x\) is a solution if it makes the left-hand side equal to zero. Checking \(x=-\sqrt2\) Substitute \(x=-\sqrt2\): \[ (-\sqrt2)^2-\sqrt2(-\sqrt2)-4 \]
Determine Whether the Given Values Are Solutions of the Equation Question: Determine whether the given values are solution of the given equation or not: \[ 2x^2-x+9=x^2+4x+3 \] (i) \(x=2\) (ii) \(x=3\) Solution A value of \(x\) is a solution if the left-hand side (LHS) becomes equal to the right-hand side (RHS). Checking \(x=2\) LHS: \[
Determine Whether the Given Values Are Solutions of the Equation Question: Determine whether the given values are solution of the given equation or not: \[ x+\frac{1}{x}=\frac{13}{6} \] (i) \(x=\frac{5}{6}\) (ii) \(x=\frac{4}{3}\) Solution A value of \(x\) is a solution if, after substitution, the left-hand side becomes equal to the right-hand side. Checking \(x=\frac{5}{6}\) Substitute \(x=\frac{5}{6}\):
Determine Whether the Given Values Are Solutions of the Equation Question: Determine whether the given values are solution of the given equation or not: \[ x^2-3\sqrt3\,x+6=0 \] (i) \(x=\sqrt3\) (ii) \(x=-2\sqrt3\) Solution A value of \(x\) is a solution if it makes the left-hand side equal to zero. Checking \(x=\sqrt3\) Substitute \(x=\sqrt3\): \[ (\sqrt3)^2-3\sqrt3(\sqrt3)+6 \]