Advertisements
Advertisements
प्रश्न
Find the third proportional to a2 – b2 and a + b.
Advertisements
उत्तर
Let the third proportional to a2 – b2 and a + b be n.
`=>` a2 – b2, a + b and n are in continued proportion.
`=>` a2 – b2 : a + b = a + b : n
`=> n = (a + b)^2/(a^2 - b^2)`
= `(a + b)^2/((a + b)(a - b))`
= `(a + b)/(a - b)`
संबंधित प्रश्न
If a, b and c are in continued proportion, prove that `(a^2 + b^2 + c^2)/(a + b + c)^2 = (a - b + c)/(a + b + c)`
If x and y be unequal and x : y is the duplicate ratio of x + z and y + z, prove that z is mean proportional between x and y.
If q is the mean proportional between p and r prove that `(p^3 + q^3 + r^3)/(p^2q^2r^2) = 1/p^3 + 1/q^3 = 1/r^3`
If u, v, w, and x are in continued proportion, then prove that (2u+3x) : (3u+4x) : : (2u3+3v3) : (3u3+4v3)
`("pqr")^2 (1/"p"^4 + 1/"q"^4 + 1/"r"^4) = ("p"^4 + "q"^4 + "r"^4)/"q"^2`
Find the mean proportion of: `(1)/(12) and (1)/(75)`
In proportion, the 1st, 2nd, and 4th terms are 51, 68, and 108 respectively. Find the 3rd term.
Find the value of x if 5 : 3 : : x : 6.
The length and breadth of a rectangular field are in the ratio 5 : 4. If the width of the field is 36 m, what is its length?
Find two numbers whose mean proportional is 16 and the third proportional is 128.
Determine if the following are in proportion.
15, 45, 40, 120
