Question

Solve it.

(√11 + √7) ( √11 - √7 ) ​

Answer 1

$= > ( \sqrt{11} + 7)( \sqrt{11} - 7)$

Identity being used,

$= > (\sqrt{a} + b )( \sqrt{a} - b) = a - {b }$

Hence,

$= > 11 - 7 \\ = > 4$

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Answer 2

Identity used is (a+b)(a-b) = a²-b²

$\begin{gathered}( \sqrt{11} + \sqrt{7}) ( \sqrt{11} - \sqrt{7} ) = \\ \\ (\sqrt{ {11})^{2} } - (\sqrt{ {7})^{2} } \\ \\ ( {11}^{ \frac{1}{2} }) {}^{2} - ({7}^{ \frac{1}{2} } ){}^{2} \\ \\ {11}^{ \frac{1}{2} \times 2} - {7}^{ \frac{1}{2} \times 2} \\ \\ 11 - 7 \\ \\ = 4\end{gathered}$

The answer is 4 as you can see the solution!

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$\begin{gathered}\boxed{\begin{array}{| c |}\qquad\tt\large\textsf{ ! Formulas ! }\\\\\\\qquad\tt{:}\longrightarrow\textsf{ ( a + b )² = a² + 2ab + b² }\\\\\qquad\tt{:}\longrightarrow\textsf{ ( a - b )² = a² - 2ab + b² }\\\\\qquad\tt{:}\longrightarrow\textsf{ a² - b² = ( a + b ) ( a - b ) }\\\\\qquad\tt{:}\longrightarrow\textsf{ ( a + b )³ = a³ + 3a²b + 3ab² }\\\\\qquad\tt{:}\longrightarrow\textsf{ ( a - b )³ = a³ - 3a²b + 3ab² - b³ }\\\\\qquad\tt{:}\longrightarrow\textsf{ a³ - b³ = ( a - b ) ( a² + ab + b² ) }\end{array}}\end{gathered}$