(a) Simplify : \[3x\left( 4x-5 \right)+3\]and find its value |
(i) x = 3 (ii) x = \[\frac{1}{2}\]: |
(b) Simplify: \[a\left( {{a}^{2}}+a+1 \right)+5\]and find its value for (a) a = 0 (b) a = 1 (c) \[a\text{ }=-1.\] |
Answer:
(a) \[3x\text{ }\left( 4x5 \right)+3\] \[=12{{x}^{2}}15x+3\] For x = 3, \[=12{{\left( 3 \right)}^{2}}15\left( 3 \right)+3\] \[=12\left( 9 \right)45+3\] \[=10845+3=66\] For x =\[\frac{1}{2}\] \[=12{{\left( \frac{1}{2} \right)}^{2}}-15\left( \frac{1}{2} \right)+3\] \[=3-\frac{15}{2}+3\] \[=6-\frac{15}{2}\] \[=\frac{12-15}{2}=\frac{-3}{2}\] (b) \[a\left( {{a}^{2}}+a+1 \right)+5=\left( a\times {{a}^{2}} \right)+\left( a\times a \right)+\left( a\times 1 \right)+5\] \[={{a}^{3}}+\text{ }{{a}^{2}}+\text{ }a+5\] For a = 0 \[=\text{ }{{\left( 0 \right)}^{3}}+{{\left( 0 \right)}^{2}}+\left( 0 \right)+5\] = 5 For a = 1 \[{{\left( 1 \right)}^{3}}+{{\left( 1 \right)}^{2}}+\left( 1 \right)+5\] \[=1+1+1+5\] = 8 For\[a\text{ }=1\] \[{{\left( 1 \right)}^{3}}+{{\left( 1 \right)}^{2}}+\left( 1 \right)+5\] \[=\text{ }1+11+5\] = 4
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