untitled

the new student =
1

1984

1

1950 34







x x

b. By the question, 1
1

1950 1984





x x

or, 1

1

1950 1984





x x

or, 1

( 1 )

1950 1950 1984



 

xx

x x

or, x^2 x 1950 x 1984 x 1950 [by cross-multiplication]
or, x^2 x 1950  34 x
? x^2  35 x 9015 0 [showed]
c.x^2  35 x 1950 0
or,x^2  65 x 30 x 1950 0
or,x(x 65 ) 30 (x 65 ) 0
or,(x 65 )(x 30 ) 0
?x 65 0 , or, x 30 0
If x 65 0 ,x  65
Again, if x 30 0 ,x 30
Since the number of students, i.e., x cannot be negative, xz 65
?x 30.

? in the first case, average = 65
30

1950

and in the second case, average = 64
31

1984

.

Exercise 5⋅ 2

1. Assuming x as the variable in the equation a^2 xb 0 , which one of the
   following is the degree of the equation?
   a. 3 b. 2 c. 1 d. 0


2. Which one of the following is an identity?

a.(x 1 )^2 (x 1 )^2 4 x b. (x 1 )^2 (x 1 )^2 2 (x^2  1 )

c.(ab)^2 (ab)^2 2 ab d. (ab)^2 a^2  2 abb^2

3. How many roots are there in the equation (x 4 )^2 0?

a. 1 b. 2 c. 3 d. 4
4. Which one of the following are the two roots of the equation x^2 x 12 0?