Prove that: x^ -1 y y^ -1 z z^ -1 x =1. - Vidyadip

Question

Prove that:
$\sqrt{\text{x}^{-1}\text{y}}\times\sqrt{\text{y}^{-1}\text{z}}\times\sqrt{\text{z}^{-1}\text{x}}=1.$

✓

Answer

$\text{L.H.S}=\sqrt{\text{x}^{-1}\text{y}}\times\sqrt{\text{y}^{-1}\text{z}}\times\sqrt{\text{z}^{-1}\text{x}}=1.$
$=\sqrt{\frac{\text{y}}{\text{x}}}\times\sqrt{\frac{\text{z}}{\text{y}}}\times\sqrt{\frac{\text{x}}{\text{z}}}$
$=\sqrt{\frac{\text{y}}{\text{x}}\times\frac{\text{z}}{\text{y}}\times\frac{\text{x}}{\text{z}}}$
$=\sqrt1$
$=1$
$=\text{R.H.S}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Numbers System→Numbers System — all question types→Maths STD 9 question papers→Gujarat Board STD 9 question papers→Gujarat Board question paper generator→

Similar questions

A vessel in the form of a hemispherical bowl is full of water. The contents are emptied into a cylinder. The internal radii of the bowl and cylinder are respectively 6cm and $4\ cm$. Find the height of water in the cylinder.

A conical pit of top diameter $3.5 \ cm$ is $12 \ m$ deep. What is its capacity in kilolitres?

Factorise: $2\text{x}^2+3\sqrt{3}\text{x}+3$

A three-wheeler scooter charges ₹ 15 for first kilometer and ₹ 8 each for every subsequent kilometer. For a distance of x km, an amount of y is paid. Write the linear equation representing the above information.

Express the decimal $0 . \overline{235}$ in the form $\frac{p}{q}$, where $p,q$ are integers and $q \neq 0$.

“If two sides and an angle of one triangle are equal to two sides and an angle of another triangle then the two triangles must be congruent.” Is the statement true? Why?

A cylindeical tub of radius $12\ cm$ contains water to a depth of $20\ cm$. A sphrical iron ball is dropped into the tub and thus the leval of water is raised by $6.75\ cm$. What is the radius of the ball.

Examine whether the following numbers are rational or irrational. $\sqrt{7}\times\sqrt{343}$

hemispherical bowl is made of steel $0.25\ cm$ thick. The inside radius of the bowl is $5\ cm$. Find the volume of steel used in making the bowl.

ABCD is a rectangle with $\angle\text{ABD}=40^\circ$. Determine $\angle\text{DBC}$.