Question
Solve the following equation:
$\sqrt{2} x ^2-3 x -2 \sqrt{2}=0$
$\sqrt{2} x ^2-3 x -2 \sqrt{2}=0$
✓
Answer
$\sqrt{2} x^2-3 x-2 \sqrt{2}=0 $
$ x^2-\frac{3}{\sqrt{2}} x-2=0 $
$x^2+\frac{1}{\sqrt{2}} x-2 \sqrt{2}-2=0$
$ x\left(x+\frac{1}{\sqrt{2}}\right)-2 \sqrt{2}\left(x+\frac{1}{\sqrt{2}}\right)=0$
$\left(x+\frac{1}{\sqrt{2}}\right)(x-2 \sqrt{2})=0 $
$\left(x+\frac{1}{\sqrt{2}}\right)=0,(x-2 \sqrt{2})=0$
$x=-\frac{1}{\sqrt{2}}, x=2 \sqrt{2}$
$ x^2-\frac{3}{\sqrt{2}} x-2=0 $
$x^2+\frac{1}{\sqrt{2}} x-2 \sqrt{2}-2=0$
$ x\left(x+\frac{1}{\sqrt{2}}\right)-2 \sqrt{2}\left(x+\frac{1}{\sqrt{2}}\right)=0$
$\left(x+\frac{1}{\sqrt{2}}\right)(x-2 \sqrt{2})=0 $
$\left(x+\frac{1}{\sqrt{2}}\right)=0,(x-2 \sqrt{2})=0$
$x=-\frac{1}{\sqrt{2}}, x=2 \sqrt{2}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The sum of the ages of Vivek and his younger brother Amit is $47$ years. The product of their ages in years is $550$. Find their ages.
→If $a: b=c: d$, then prove that $\frac{a^2+a b+b^2}{a^2-a b+b^2}=\frac{c^2+c d+d^2}{c^2-c d+d^2}$
→In following figure , chord ED is parallel to the diameter AC of the circle. Given ∠ CBE = 65° , calculate ∠DEC .
A straight line makes positive intercepts on the co-ordinates axes whose sum is 7 . If the line passes through the point $(-3,8)$, find its equation.
→Given ∠BAC (Fig), determine the locus of a point which lies in the interior of ∠BAC and equidistant from two lines AB and AC.
The angle of elevation of a stationary cloud from a point 25m above a lake is 30° and the angle of depression of its reflection in the lake is 60°. What is the height of the cloud above the lake-level?
If $( a+c) : b = 5 : 1$ and $(bc + cd) : bd = 5 : 1,$ then prove that $a : b = c : d$
→Find the values of $a$ and $b$ when the polynomial $f(x)=a x^3+3 x^2+b x-3$ is exactly divisible by $(2 x+3)$ and leaves a remainder $-3$ when divided by $(x+2)$.
→A point A is $17\ cm$ from the centre of the circle. The length of the tangent drawn from A to the circle is $15\ cm$. find the radius of the circle.
→The scale of a model ship is $1 : 300.$
$(i)$ If the length of the model is $250 \ cm,$ find the actual length in $m.$
$(ii)$ If the deck area of the model is $1 m^2,$ find the deck area of the ship and the cost of painting it at $₹10$ per $m^2.$
$(iii)$ If the volume of the ship is $10,80,00,000 m^3,$ find the volume of the model.
→$(i)$ If the length of the model is $250 \ cm,$ find the actual length in $m.$
$(ii)$ If the deck area of the model is $1 m^2,$ find the deck area of the ship and the cost of painting it at $₹10$ per $m^2.$
$(iii)$ If the volume of the ship is $10,80,00,000 m^3,$ find the volume of the model.