Solution: We have $A=\left(\begin{array}{ll}4 & 0 \\ 2 & 5\end{array}\right)$. To get the inverse we will proceed by augmented matrix with elementary row transformation process is as follow:...
Solve: (x^2+1/x^2)-3(x-1/x)-2=0
Let \[\left( x\text{ }\text{ }1/x \right)\text{ }=\text{ }y\text{ }\ldots .\text{ }\left( 1 \right)\] squaring on both sides \[{{\left( x\text{ }\text{ }1/x \right)}^{2}}~=\text{ }{{y}^{2}}\] or,...
Solve: 2(x^2+1/x^2)-(x+1/x)=11
let \[\left( x\text{ }+\text{ }1/x \right)\text{ }=\text{ }y\text{ }\ldots .\text{ }\left( 1 \right)\] squaring on both sides \[{{\left( x\text{ }+\text{ }1/x \right)}^{2}}~=\text{ }{{y}^{2}}\]...
Solve:9(x^2+1/x^2)-9(x+1/x)-52=0
Let, \[~\left( x\text{ }+\text{ }1/x \right)\text{ }=\text{ }y\text{ }\ldots .\text{ }\left( 1 \right)\] squaring both sides \[{{\left( x\text{ }+\text{ }1/x \right)}^{2}}~=\text{ }{{y}^{2}}\]...
Solve: x4 – 2×2 – 3 = 0
According to ques, \[{{x}^{4}}~\text{ }2{{x}^{2}}~\text{ }3\text{ }=\text{ }0\] Let’s take \[{{x}^{2}}~=\text{ }y\] Then, the equation becomes \[{{y}^{2}}~\text{ }2y\text{ }\text{ }3\text{ }=\text{...
Solve : 2×4 – 5×2 + 3 = 0
According to ques, \[~2{{x}^{4}}~\text{ }5{{x}^{2}}~+\text{ }3\text{ }=\text{ }0\] Let \[{{x}^{2}}~=\text{ }y\] The, \[2{{y}^{2}}~\text{ }5y\text{ }+\text{ }3\text{ }=\text{ }0\] \[2{{y}^{2}}~\text{...
Solve: x + 4/x = -4; x ≠ 0
According to ques, \[~x\text{ }+\text{ }4/x\text{ }=\text{ }-4\] or, \[\left( {{x}^{2~}}+\text{ }4 \right)/\text{ }x\text{ }=\text{ }-4\] Or, \[{{x}^{2}}~+\text{ }4\text{ }=\text{ }-4x\] or,...
Solve: x2 – 11/4 x + 15/8 = 0
According to ques, \[~{{x}^{2}}~\text{ }11/4\text{ }x\text{ }+\text{ }15/8\text{ }=\text{ }0\] Taking L.C.M , \[\left( 8{{x}^{2}}~\text{ }22x\text{ }+\text{ }15 \right)/\text{ }8\text{ }=\text{ }0\]...
Solve : a2x2 – b2 = 0
According to ques, \[{{a}^{2}}{{x}^{2}}~\text{ }{{b}^{2}}~=\text{ }0\] or, \[{{\left( ax \right)}^{2}}~\text{ }{{b}^{2}}~=\text{ }0\] Or, \[\left( ax\text{ }+\text{ }b \right)\left( ax\text{ }\text{...
Solve: (2x + 3)2 = 81
According to ques, \[{{\left( 2x\text{ }+\text{ }3 \right)}^{2}}~=\text{ }81\] Taking square root both sides, \[2x\text{ }+\text{ }3\text{ }=\text{ }\pm \text{ }9\] Or, \[2x\text{ }=\text{ }\pm...
Solve each of the following equations: 2x/x-3+1/2x+3+3x+9/(x-3)(2x+3)=0; x$\ne $ 3,x$\ne $ -3/2
According to ques, \[4{{x}^{2}}~+\text{ }6x\text{ }+\text{ }x\text{ }\text{ }3\text{ }+\text{ }3x\text{ }+\text{ }9\text{ }=\text{ }0\] Or, \[4{{x}^{2}}~+\text{ }10x\text{ }+\text{ }6\text{ }=\text{...