Advertisements
Advertisements
प्रश्न
Find the third proportional to:
`a/b + b/c, sqrt(a^2 + b^2)`.
Advertisements
उत्तर
Let x be the third proportional then
`a/b + b/c, sqrt(a^2 + b^2) = sqrt(a^2 + b^2) : x`
⇒ `(a^2 + b^2)/(ab) : sqrt(a^2 + b^2) = sqrt(a^2 + b^2) : x`
⇒ `(a^2 + b^2)/(ab sqrt(a^2 + b^2)) = sqrt(a^2 + b^2)/x`
⇒ x = `(ab (a^2 + b^2))/((a^2 + b^2))`
⇒ x = ab.
APPEARS IN
संबंधित प्रश्न
Find the third proportional to `x/y + y/x` and `sqrt(x^2 + y^2)`
What least number must be added to each of the numbers 5, 11, 19 and 37, so that they are in proportion?
Write (T) for true and (F) for false in case of the following:
32 kg : Rs 36 : : 8 kg : Rs 9
The 1st, 3rd, and 4th terms of a proportion are 12, 8, and 14 respectively. Find the 2nd term.
If 9, x, x 49 are in proportion, find the value of x.
If a, b, c and d are in proportion, prove that: `(a^2 + ab)/(c^2 + cd) = (b^2 - 2ab)/(d^2 - 2cd)`
If a, b, c and d are in proportion, prove that: `(a + c)^3/(b + d)^3 = (a(a - c)^2)/(b(b - d)^2)`
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)`
If a, b, c are in continued proportion, prove that: a : c = (a2 + b2) : (b2 + c2)
Write True (T) or False (F) against the following statement:
5.2 : 3.9 : : 3 : 4
