## NCERT Exercise 4.3

### Part 3

Question 3: Find the roots of the following equations:

Question (i): x-1/x=3: x≠0

Solution:

x-1/x=3

Or, (x^2-1)/(x)=3

Or, x^2-3x-1=0

We have; a = 1, b = - 3 and c = - 1

Root can be calculated as follows:

text(Root)=(-b±sqrt(b^2-4ac))/(2a)

=(3±sqrt((-3)^2-4xx1xx-1))/(2xx1)

=(3±sqrt(13))/(2)

Hence, α=(3+sqrt(13))/(2)

And, β=(3-sqrt(13))/(2)

Question (ii): (1)/(x+4)-(1)/(x-7)=(11)/(30) x≠-4 or 7

Solution:

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

Or, (x-7-x-4)/((x+4)(x-7))=(11)/(30)

Or, (x^2-7x+4x-28)/(30)=-1

Or, x^2-3x-28=-30

Or, x^2-3x-28+30=0

Or, x^2-3x+2=0

Or, x^2-2x-x+2=0

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

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

Hence,roots are; 1 and 2

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

Solution: Let us assume, Rehman’s present age = x

Therefore, 3 years ago, Rehman’s age = x – 3

And, 5 years from now, Rehman’s age = x + 5

As per question;

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

Or, (x+5+x-3)/((x-3)(x+5))=1/3

Or, (2x+2)/(x^2+5x-3x-15)=1/3

Or, 6x+6=x^2+2x-15

Or, x^2+2x-15-6x-6=0

Or, x^2-4x-21=0

Or, x^2-7x+3x-21=0

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

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

Ruling out the negative value; Rehman’s Age = 7 year