If x3-y5-z4- 5x-3y-4zP- Find the value of P-

Given nbsp;x3=y5=z4= 5 x 3y+4zP nbsp; Consider x3=y5=z4 ⇒5× x5× 3= 3× y 3× 5=4× z4× 4 ⇒5x15= 3y 15=4z16=5x 3y+4z15 15+16 (Using theorem of equal ratios) ⇒ ...

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Standard IX

Mathematics

Theorems on Equal Ratios

If x3=y5=z4= ...

Question

If $\frac{x}{3} = \frac{y}{5} = \frac{z}{4} = \frac{5 x - 3 y + 4 z}{P}$ . Find the value of $P$ ?

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Solution

Given $\frac{x}{3} = \frac{y}{5} = \frac{z}{4} = \frac{5 x - 3 y + 4 z}{P}$
Consider $\frac{x}{3} = \frac{y}{5} = \frac{z}{4}$
$\Rightarrow \frac{5 \times x}{5 \times 3} = \frac{- 3 \times y}{- 3 \times 5} = \frac{4 \times z}{4 \times 4}$

$\Rightarrow \frac{5 x}{15} = \frac{- 3 y}{- 15} = \frac{4 z}{16} = \frac{5 x - 3 y + 4 z}{15 - 15 + 16}$ (Using theorem of equal ratios)

$\Rightarrow \frac{x}{3} = \frac{y}{5} = \frac{z}{4} = \frac{5 x - 3 y + 4 z}{16}$
Hence $P = 16$ .

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If x3=y5=z4=5x−3y+4zP. Find the value of P?

Given x3=y5=z4=5x−3y+4zP Consider x3=y5=z4 ⇒5×x5×3=−3×y−3×5=4×z4×4 ⇒5x15=−3y−15=4z16=5x−3y+4z15−15+16 (Using theorem of equal ratios) ⇒x3=y5=z4=5x−3y+4z16 Hence P=16.

If $\frac{x}{3} = \frac{y}{5} = \frac{z}{4} = \frac{5 x - 3 y + 4 z}{P}$ . Find the value of $P$ ?