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3 years ago

What is the following product?

Mathematics

1 answer:

KiRa [710]3 years ago

5 0

ANSWER

$2 \sqrt{42} +7 \sqrt{2}- 6- \sqrt{21}$

EXPLANATION

The given product is:

$( \sqrt{14} - \sqrt{3} )( \sqrt{12} + \sqrt{7} )$

We expand using the distributive property to obtain:

$\sqrt{14}( \sqrt{12} + \sqrt{7}) -\sqrt{3}( \sqrt{12} + \sqrt{7} )$

Extract the perfect squares to get:

$\sqrt{14}(2 \sqrt{3} + \sqrt{7}) -\sqrt{3}( 2\sqrt{3} + \sqrt{7} )$

Expand further to get;

$2 \sqrt{42} +7 \sqrt{2}- 2(3) - \sqrt{21}$

This simplifies to,

$2 \sqrt{42} +7 \sqrt{2}- 6- \sqrt{21}$

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Explanation

Step 1

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Step 2

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a) now, replace the x an z value sfrom equation (2) and (3) into equation(1)

$\begin{gathered} x+y+z=3084\Rightarrow\text{ Equation(1)} \\ (y-76)+y+(y+379)=3084 \\ -76+3y+379=3084 \\ 303+3y=3084 \\ 3y=3084-303 \\ \\ 3y=2781 \\ \text{divide both sides by 3} \\ \frac{3y}{3}=\frac{2781}{3} \\ y=927 \end{gathered}$

now, replace the y value in equatino (2) to find x

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c) finally, prelace x and y value in equation (1) to find z

$\begin{gathered} x+y+z=3084\Rightarrow\text{ Equation(1)} \\ 851+927+z=3084 \\ \text{add like terms} \\ 1778+z=3084 \\ \text{subtract 1778 in both sides} \\ 1778+z-1778=3084-1778 \\ z=1306 \end{gathered}$

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middle side:927

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