Find the product- 3- 2 2- 3 3- 2 2- 3 -

We have, ( 3+√(2))( 2+√(3) #10;)( 3 √(2))( 2 √(3)) #10; #10; =( 3+√(2))( 3 √(2) #10;)( 2+√(3))( 2 √(3)) #10; #10; =[ 3^2 ( √(2) #10; ...

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Operations on Rational and Irrational Numbers

Find the prod...

Question

Find the product: $(3 + \sqrt{2}) (2 + \sqrt{3}) (3 - \sqrt{2}) (2 - \sqrt{3}) .$

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Solution

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(3 + \sqrt{2}) (2 + \sqrt{3}) (3 - \sqrt{2}) (2 - \sqrt{3})

∣ ∣ ∣ \begin{matrix} \sqrt{2} & 2 \sqrt{3} 3 \sqrt{2} & \sqrt{3} \end{matrix} ∣ ∣ ∣

Find the sum to n terms of the series $\frac{3}{1^{2} \times 2^{2}} + \frac{5}{2^{2} \times 3^{3}} + \frac{7}{3^{2} \times 4^{2}} . . . . . .$ is

1 + \frac{1^{2} + 2^{2}}{2!} + \frac{1^{2} + 2^{2} + 3^{3}}{3!} + \frac{1^{2} + 2^{2} + 3^{2} + 4^{2}}{4!} + . . . . .

\frac{1^{2} + 2^{2}}{| 3 - -} + \frac{1^{2} + 2^{2} + 3^{2}}{| 4 - -} + \frac{1^{2} + 2^{2} + 3^{3} + 4^{2}}{| 5 - -} . . . . . . . .

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