Evaluate
-2\sqrt{15}\approx -7.745966692
Expand
-2\sqrt{15}
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\left(\sqrt{3}\right)^{2}-2\sqrt{3}\sqrt{5}+\left(\sqrt{5}\right)^{2}-8
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sqrt{3}-\sqrt{5}\right)^{2}.
3-2\sqrt{3}\sqrt{5}+\left(\sqrt{5}\right)^{2}-8
The square of \sqrt{3} is 3.
3-2\sqrt{15}+\left(\sqrt{5}\right)^{2}-8
To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.
3-2\sqrt{15}+5-8
The square of \sqrt{5} is 5.
8-2\sqrt{15}-8
Add 3 and 5 to get 8.
-2\sqrt{15}
Subtract 8 from 8 to get 0.
\left(\sqrt{3}\right)^{2}-2\sqrt{3}\sqrt{5}+\left(\sqrt{5}\right)^{2}-8
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sqrt{3}-\sqrt{5}\right)^{2}.
3-2\sqrt{3}\sqrt{5}+\left(\sqrt{5}\right)^{2}-8
The square of \sqrt{3} is 3.
3-2\sqrt{15}+\left(\sqrt{5}\right)^{2}-8
To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.
3-2\sqrt{15}+5-8
The square of \sqrt{5} is 5.
8-2\sqrt{15}-8
Add 3 and 5 to get 8.
-2\sqrt{15}
Subtract 8 from 8 to get 0.
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Simultaneous equation
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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