Advertisements
Advertisements
Question
Find the fourth proportional to:
x3 - y2, x4 + x2y2 + y4, x - y.
Advertisements
Solution
Let A be the fourth proportional then
x3 - y2 : x4 + x2y2 + y4 = x - y : A
⇒ `(x^3 - y^3)/(x^4 + x^2y^2 + y^4) = (x - y)/"A"`
⇒ A(x3 - y3) = (x - y)(x4 + x2y2 + y4)
⇒ A = `((x - y)(x^4 + x^2y^2 + y^4))/(x^3 - y^3)`
⇒ A = `((x - y)(x^2 + y^2 + xy)(x^2 + y^2 - xy))/((x - y)(x^2 + xy + y^2)`
⇒ A = x2 + y2 - xy.
RELATED QUESTIONS
Using properties of proportion, solve for x. Given that x is positive:
`(2x + sqrt(4x^2 -1))/(2x - sqrt(4x^2 - 1)) = 4`
If three quantities are in continued proportion; show that the ratio of the first to the third is the duplicate ratio of the first to the second.
Given four quantities a, b, c and d are in proportion. Show that: (a – c)b2 : (b – d)cd = (a2 – b2 – ab) : (c2 – d2 – cd)
Find the third proportion to the following :
16x2 and 24x
If 2x – 1, 5x – 6, 6x + 2 and 15x – 9 are in proportion, find the value of x.
Determine if the following numbers are in proportion:
32, 48, 70, 210
Determine if the following numbers are in proportion:
150, 200, 250, 300
Find the value of x in each of the following proportions:
x : 92 : : 87 : 116
Write (T) for true and (F) for false in case of the following:
30 bags : 18 bags : : Rs 450 : Rs 270
If a, b, c and d are in proportion, prove that: `(a^2 + ab + b^2)/(a^2 - ab + b^2) = (c^2 + cd + d^2)/(c^2 - cd + d^2)`
