Ifx-3x-y-z- y-3y-z-x-z-3z-x-y and x - y - z - 0- then show that the value of each ratio is equal to 1- -3 Marks-

Let x/3x−y−z= y/3y−z−x=z/3z−x−y=k By theorem of equal ratios, k=x+y+z/(3x−y−z)+(3y−z−x)+(3z−x−y) nbsp;[1 Mark] ⇒ k=x+y+z/(3x−x−x)+(3y−y−y)+(3z−z−z) nbsp;[1 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VII

Mathematics

Equivalent Ratios

Ifx/3x−y−z= y...

Question

If  $\frac{x}{3 x - y - z} =$ $\frac{y}{3 y - z - x} =$ $\frac{z}{3 z - x - y}$ and $x + y + z \neq 0$ , then show that the value of each ratio is equal to 1. [3 Marks]

Open in App

Solution

Let $\frac{x}{3 x - y - z} =$ $\frac{y}{3 y - z - x} =$ $\frac{z}{3 z - x - y} = k$
By theorem of equal ratios,
$k = \frac{x + y + z}{(3 x - y - z) + (3 y - z - x) + (3 z - x - y)}$ [1 Mark]
$\Rightarrow k = \frac{x + y + z}{(3 x - x - x) + (3 y - y - y) + (3 z - z - z)}$ [1 Mark]
$\Rightarrow k = \frac{x + y + z}{x + y + z}$
$\Rightarrow k = 1$
∴ Each ratio = 1 [1 Mark]

Suggest Corrections

Similar questions

Q. If

\frac{x}{y + z - x} = \frac{y}{z + x - y} = \frac{z}{x + y - z}

and x + y + z

\neq

0 then show that each ratio is equal to 1.

Q. In the given figure, if AB || CD, CD || EF and y : z = 3 : 7, find x.

Q.  Solve:

\sqrt[5]{x^{20} y^{- 10} z^{5}} \div \frac{x^{3}}{y^{3}}

Q.  Find the values of x and y, if

[\begin{matrix} 3 x - y 5 \end{matrix}] = [\begin{matrix} 7 x + y \end{matrix}]

Q. Simplify the polynomials A and B and find

\frac{A}{B}

.

A = 3

y^{3}

+ 5

y^{3}

-

y^{3}

B = 6

y^{2}

- 4

y^{2}

+ 3

y^{2}

- 7

y^{2}

Join BYJU'S Learning Program

If  x3x−y−z= y3y−z−x=z3z−x−y and x+y+z≠0, then show that the value of each ratio is equal to 1. [3 Marks]

Let x3x−y−z= y3y−z−x=z3z−x−y=k By theorem of equal ratios, k=x+y+z(3x−y−z)+(3y−z−x)+(3z−x−y) [1 Mark] ⇒k=x+y+z(3x−x−x)+(3y−y−y)+(3z−z−z) [1 Mark] ⇒k=x+y+zx+y+z ⇒k=1 ∴ Each ratio = 1 [1 Mark]

If  $\frac{x}{3 x - y - z} =$ $\frac{y}{3 y - z - x} =$ $\frac{z}{3 z - x - y}$ and $x + y + z \neq 0$ , then show that the value of each ratio is equal to 1. [3 Marks]