Advertisements
Advertisements
Question
If x + 5 is the mean proportion between x + 2 and x + 9, find the value of x.
Advertisements
Solution
∵ x + 5 is the mean proportion between x + 2 and x + 9, then
(x + 5)² = (x + 2) (x + 9)
⇒ x² + 10x + 25 = x² + 11x + 18
⇒ x² + 10x – x² – 11x = 18 – 25
⇒ – x = – 7
∵ x = 7.
APPEARS IN
RELATED QUESTIONS
If b is the mean proportion between a and c, show that: `(a^4 + a^2b^2 + b^4)/(b^4 + b^2c^2 + c^4) = a^2/c^2`.
If a, b, c and d are in proportion prove that `(13a + 17b)/(13c + 17d) = sqrt((2ma^2 - 3nb^2)/(2mc^2 - 3nd^2)`
If `(4m + 3n)/(4m - 3n) = 7/4`, use properties of proportion to find m : n
Find the fourth proportional to `(1)/(3), (1)/(4), (1)/(5)`
Write (T) for true and (F) for false in case of the following:
45 km : 60 km : : 12 h : 15 h
If a, b, c are in continued proportion, prove that: `(a + b)/(b + c) = (a^2(b - c))/(b^2(a - b)`.
A car travels 90 km in 3 hours with constant speed. It will travel 140 km in 5 hours at the same speed
Write the mean and extreme terms in the following ratios and check whether they are in proportion.
400 gm is to 50 gm and 25 rupees is to 625 rupees
10 g of caustic soda dissolved in 100 mL of water makes a solution of caustic soda. Amount of caustic soda needed for 1 litre of water to make the same type of solution is ______.
Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
200 mL : 2.5 litre and ₹ 4 : ₹ 50
