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प्रश्न
Using properties of proportion, solve for x:
`(sqrt(x + 5) + sqrt(x - 16))/(sqrt(x + 5) - sqrt(x - 16)) = 7/3`
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उत्तर
`(sqrt(x + 5) + sqrt(x - 16))/(sqrt(x + 5) - sqrt(x - 16)) = 7/3`
Applying componendo and dividendo,
`(sqrt(x + 5)+ sqrt(x - 16) + sqrt(x + 5) - sqrt(x - 16))/(sqrt(x + 5)+sqrt(x - 16) - sqrt(x + 5) + sqrt(x -16)) = (7 + 3)/(7 - 3)`
`(2sqrt(x + 5))/(2sqrt(x - 16)) = 10/4`
`sqrt(x + 5)/sqrt(x - 16) = 5/2`
Squaring both sides,
`(x + 5)/(x - 16) = 25/4`
4x + 20 = 25x – 400
21x = 420
`x = 420/21 = 20`
संबंधित प्रश्न
If `a/b = c/d` prove that each of the given ratios is equal to
`(5a + 4c)/(5b + 4d)`
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(p2q - qr2 ), (pqr - pr2 ) and (pq2 - pr2)
Find the third proportion to the following :
(x - y) and m (x - y)
Given four quantities p, q, r and s are in proportion, show that
q2(p - r) : rs (q - s) =(p2- q2- pq): ( r2-s2-rs).
If p, q and r in continued proportion, then prove the following:
(p2 - q2)(q2 + r2) = (q2 - r2)(p2 + q2)
If 9, x, x 49 are in proportion, find the value of x.
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If a, b, c are in continued proportion, prove that: `(1)/a^3 + (1)/b^3 + (1)/c^3 = a/(b^2c^2) + b/(c^2a^2) + c/(a^2b^2)`
Find the missing number in the box in the proportion:
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Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
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