If-P-Q-R-2-3-4-and-P-2-Q-2-R-2-11600-then-find-P-Q-R-

Question Number 16383 by aamaguestt last updated on 21/Jun/17

If P : Q : R = 2 : 3 : 4 and P^{2} + Q^{2} + R^{2} = 11600,

then find (P + Q - R) .

Answered by ajfour last updated on 21/Jun/17

p^{2} [1 + {(\frac{q}{p})}^{2} + {(\frac{r}{p})}^{2}] = 29 \times 400

p^{2} [1 + \frac{9}{4} + 4] = 29 \times 400

\Rightarrow p^{2} = \frac{29 \times 400 \times 4}{29} = 1600

{(p + q - r)}^{2} = p^{2} + q^{2} + r^{2} + 2 (p q - q r - r p)

?^{2} = 29 \times 400 + 2 p^{2} [\frac{q}{p} - (\frac{q}{p}) (\frac{r}{p}) - \frac{r}{p}]

= 29 \times 400 + 2 \times 1600 [\frac{3}{2} - \frac{3}{2} \times 2 - 2]

?^{2} = 29 \times 400 + 2 \times 1600 (- \frac{7}{2})

?^{2} = 400 (29 - 28) = 400

? = \pm 20 .

Commented by chux last updated on 21/Jun/17

mr Ajfour \dots . I love this style .

Commented by ajfour last updated on 21/Jun/17

i c a l l i t c o n v e n i e n c e . ., t h a n k s .

Commented by chux last updated on 21/Jun/17

exactly \dots . thats the word .

Answered by RasheedSoomro last updated on 21/Jun/17

P : Q : R = 2 : 3 : 4

P^{2} + Q^{2} + R^{2} = 11600

P + Q - R = ?

- - - - - - - - - - - - - - - - - - - - - -

Let P = 2 k, Q = 3 k and R = 4 k

{(2 k)}^{2} + {(3 k)}^{2} + {(4 k)}^{2} = 11600

{29 k}^{2} = 11600

k^{2} = \frac{11600}{29} = 400

k = \pm 20

P + Q - R = 2 k + 3 k - 4 k = k = \pm 20

Commented by ajfour last updated on 21/Jun/17

m u c h b e t t e r s i r .

Commented by RasheedSoomro last updated on 21/Jun/17

Not better sir, only a different way .