Advertisements
Advertisements
प्रश्न
What quantity must be added to each term of the ratio a + b: a - b to make it equal to (a + b)2 : (a - b)2 ?
Advertisements
उत्तर
Let the quantity to be added be x.
Then
`((a + b) + x)/((a - b) + x) = (a + b)^2/(a - b)^2`
⇒ (a + b) (a - b)2 + (a - b)2.x
= (a + b)2 (a - b) + (a + b)2.x
⇒ [(a + b)2 - (a - b)2]x
= (a2 - b2) (a - b) - (a2 - b2) (a + b)
⇒ (4abx) = (a2 - b2) [(a - b) - (a + b)]
⇒ x = `(-2b(a^2 - b^2))/(4ab) = (b^2 - a^2)/(2a)`.
APPEARS IN
संबंधित प्रश्न
If q is the mean proportional between p and r, prove that
`p^2 - q^2 + r^2 = q^4[(1)/p^2 - (1)/q^2 + (1)/r^2]`.
Find the third proportional to `5(1)/(4) and 7.`
The ratio of boys and girls in a school is 12 : 5. If the number of girls is 840, the total strength of the school is
If 40 men can finish a piece of work in 26 days, how many men will be required to finish it in 20 days?
If a, b, c are in continued proportion, prove that: `(a + b)/(b + c) = (a^2(b - c))/(b^2(a - b)`.
If a, b, c are in continued proportion, prove that: a2 b2 c2 (a-4 + b-4 + c-4) = b-2(a4 + b4 + c4)
If a, b, c are in continued proportion, prove that: abc(a + b + c)3 = (ab + bc + ca)3
5 : `square` : : 10 : 8 : : 15 : `square`
A particular high school has 1500 students 50 teachers and 5 administrators. If the school grows to 1800 students and the ratios are maintained, then find the number of teachers and administrators
In the proportional statement p : q :: r : s, which pair of terms represents the means, and which pair represents the extremes?
