QQuestion
Using componendo and dividendo, solve for x:
\frac{\sqrt{2x+2}+\sqrt{2x-1}}{\sqrt{2x+2}-\sqrt{2x-1}} = 3
ICSEClass 10MathematicsRatio And Proportion03 Mark2023 Easy
✓Answer
Given:
\frac{\sqrt{2x+2}+\sqrt{2x-1}}{\sqrt{2x+2}-\sqrt{2x-1}}=3Applying componendo and dividendo:
\frac{(\sqrt{2x+2}+\sqrt{2x-1})+(\sqrt{2x+2}-\sqrt{2x-1})}{(\sqrt{2x+2}+\sqrt{2x-1})-(\sqrt{2x+2}-\sqrt{2x-1})}=\frac{3+1}{3-1}⇒ \frac{2\sqrt{2x+2}}{2\sqrt{2x-1}}=\frac{4}{2}
⇒ \frac{\sqrt{2x+2}}{\sqrt{2x-1}}=2
⇒ √(2x + 2) = 2√(2x − 1)
Squaring both sides:
⇒ 2x + 2 = 4(2x − 1)
⇒ 2x + 2 = 8x − 4
⇒ 8x − 2x = 2 + 4
⇒ 6x = 6
⇒ x = 1
Therefore, x = 1.
Was this answer helpful?
Related Questions
More ICSE Easy level questions
1/12
What number must be added to each of the numbers 4, 6, 8 and 11 so that the resulting four numbers are in proportion?
The mean proportional between 4 and 9 is: (a) 4 (b) 6 (c) 9 (d) 36
If x = , a ≠ b, (a) Find: (b) Using properties of proportion, find:
(x + 3), 1, (3x − 7) and −5 are in proportion. The value of x is : (a) −1 (b) 1 (c) −5 (d) 5
Using properties of proportion, find x: , x ≠ 0.
State True or False: The compound ratio of 2ab : c², bc : a² and ca : 2b2 is 1 : 1.
If = 1, then find the value of .
If a : b = b : c, prove that = 1
If the fourth and fifth of the five numbers in continued proportion are 54 and 162 respectively, find the first number.
If : (a) Find . (b) Hence, using properties of proportion, find a : b.
The following table shows the distance travelled by a train moving with uniform speed: Distance (m) 60 90 y Time (s) 2 x 5 The values of x and y are: (a) x = 4, y = 150 (b) x = 3, y = 100 (c) x = 4, y = 100 (d) x = 3, y = 150
Find the mean proportion of xy² and xz²