10th cbse maths solution for exercise 4.3 part 2

This page 10th cbse maths solution for exercise 4.3 part 2 is going to provide you solution for every problems that you find in the exercise no 4.3 part 2

10th CBSE maths solution for Exercise 4.3 part 2

(3) Find the roots of the following equations:

 (i) x - (1/x) = 3,  x ≠ 0

Solution:

  (x² - 1)/x = 3

  x² - 1 = 3 x

x² - 3 x - 1 = 0

a = 1  b = -3  c = -1

   x = - b ± √(b² - 4 a c)/2a

   x = - (-3) ± √((-3)² - 4 (1)(-1))/2(1)

   x = 3 ± √(9+4)/2

   x = (3 ± √13)/2


 (ii) [1/(x + 4)] - [1/(x -7)] = 11/30

Solution:

[1/(x + 4)] - [1/(x -7)] = 11/30

[(x - 7) - (x + 4)]/(x + 4)(x - 7) = 11/30

(x - 7 - x - 4)/(x² + 4 x - 7 x - 28) = 11/30

-11/(x² - 3 x - 28) = 11/30

30 (-11) = 11 (x² - 3 x - 28)

  -30 = x² - 3 x - 28

  x² - 3 x - 28 + 30 = 0

  x² - 3 x + 2  = 0

  x² - 1 x - 2 x + 2  = 0

   x (x - 1) - 2 (x - 1)  = 0

(x - 2) (x - 1) = 0

 x - 2 = 0        x - 1 = 0

  x = 2       x = 1


(4) The sum of the reciprocals of Rehman's ages (in years) 3 years ago and 5 years from now is 1/3. Find his present age.

Solution:

Let 'x' be Rehman's present age

Three years ago his age was 'x - 3'

5 years after his age will be 'x + 5'

Sum of the reciprocals of Rehman's ages = 1/3

[1/(x -3) + 1/(x + 5)] = 1/3

 (x + 5 + x - 3)/(x-3)(x + 5) = 1/3

 (2 x + 2)/(x² - 3 x + 5 x - 15) = 1/3

  (2 x + 2)/(x² + 2 x - 15) = 1/3

3 (2 x + 2) = 1 (x² + 2 x - 15)

 6 x + 6 = x² + 2 x - 15

x² + 2 x - 15 - 6 x - 6 = 0

x²- 4 x - 21 = 0

x² - 7 x + 3 x - 21 = 0

x (x - 7) + 3 (x - 7) = 0

(x + 3) (x - 7) = 0

 x = 3  or x = 7

So his present age will be 7 years.


(5) In a class test,the sum of Shefali's marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.

Solution:

Let 'x' be the mark got by Shefali in the subject mathematics

let '30 - x' be the mark got by Shefali in English

(x + 2)(30 - 3 - x) = 210

(x + 2)(27 - x) = 210

27 x - x² + 54 - 2 x - 210 = 0

- x² + 25 x - 156 = 0

multiplying the whole equation by (-)

x² - 25 x + 156 = 0

x² - 12 x - 13 x + 156 = 0

x (x - 12) - 13 (x - 12) = 0

(x - 12) (x - 13) = 0

x - 12 = 0          x - 13 = 0

x = 12           x = 13

if Shefali's mathematics marks = 12 then

her English mark will be = 30 - 12 = 18

if Shefali's mathematics marks = 13 then

her English mark will be = 30 - 13 = 17




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