Page 17 - CHAPTER 4 (Quadratic equations)

CHAPTER 4
QUADRATIC EQUATIONS

x+10+x 8 2x+10 8
⇒ = ⇒ =
x(x+10) 75 x²+10x 75

⇒150x+750=8x²+80x ⇒8x²-70x-750=0

⇒4x²-35x-375=0 ⇒4x²-60x+25x-375=0

⇒4x (x-15)+ 25 (x-15)= 0 ⇒(x-15)(4x+25)= 0

-25
⇒x=15 or x=
4

But the time cannot be negative.

Hence, the larger tap takes 15 hours, and the smaller tap takes 25 hours.

Example 7: 300 bananas are divided equally among a certain number

of students. If there are 10 more students, each will have receive one

banana less. Find the total number of students.

Sol: Let the number of students is x. Then,

The number of bananas received by each student = 300
x
If there are 10 more students, i.e., ( + 10) students. Then,

The number of bananas received by each student = 300
x+10

According to the question, 300 - 300 =1
x x+10
300x+3000-300x
⇒ =1 ⇒3000=x²+10x
x (x+10)

⇒x²+10x-3000=0 ⇒x²+60x-50x-3000=0

⇒x(x+60)- 50(x+60)= 0 ⇒(x+60)(x-50)= 0

⇒x= -60 or x=50

But the number of students cannot be negative.

Hence, the number of students is 50.

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