Find sum of the following surds- -x - 2-y- 2-x - 3-y- 3-x - -y-

The sum of the given surds can be determined as follows: (√( x ) +2√( y ) )+(2√( x ) 3√( y ) )+(3√( x ) +√( y ) )=(√( x ) +2√( x ) +3√( x ) )+(2√( y ) +√( ...

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Byju's Answer

Standard XII

Mathematics

Integration by Substitution

Find sum of t...

Question

Find sum of the following surds:
$(\sqrt{x} + 2 \sqrt{y}), (2 \sqrt{x} - 3 \sqrt{y}), (3 \sqrt{x} + \sqrt{y})$ .

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Solution

The sum of the given surds can be determined as follows:
$(\sqrt{x} + 2 \sqrt{y}) + (2 \sqrt{x} - 3 \sqrt{y}) + (3 \sqrt{x} + \sqrt{y}) = (\sqrt{x} + 2 \sqrt{x} + 3 \sqrt{x}) + (2 \sqrt{y} + \sqrt{y} - 3 \sqrt{y})$
$= \sqrt{x} (1 + 2 + 3) + \sqrt{y} (2 + 1 - 3) = 6 \sqrt{x} + 0 \sqrt{y} = 6 \sqrt{x}$

Hence, $(\sqrt{x} + 2 \sqrt{y}) + (2 \sqrt{x} - 3 \sqrt{y}) + (3 \sqrt{x} + \sqrt{y}) = 6 \sqrt{x}$ .

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Find sum of the following surds:(√x+2√y),(2√x−3√y),(3√x+√y).

The sum of the given surds can be determined as follows:(√x+2√y)+(2√x−3√y)+(3√x+√y)=(√x+2√x+3√x)+(2√y+√y−3√y)=√x(1+2+3)+√y(2+1−3)=6√x+0√y=6√x Hence, (√x+2√y)+(2√x−3√y)+(3√x+√y)=6√x.

Find sum of the following surds:
$(\sqrt{x} + 2 \sqrt{y}), (2 \sqrt{x} - 3 \sqrt{y}), (3 \sqrt{x} + \sqrt{y})$ .