Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th

# From a group of 2x2 black bees , square root of half of the group went to a tree. Again eight-ninth of the bees went to the same tree. The remaining two got caught up in a fragrant lotus. How many b - Mathematics

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From a group of 2x2 black bees, square root of half of the group went to a tree. Again eight-ninth of the bees went to the same tree. The remaining two got caught up in a fragrant lotus. How many bees were there in total?

#### Solution

Total numbers of black bees = 2x

Half of the group = 1/2 xx 2x^2 = x2

Square root of half of the group = sqrt(x^2) = x

Eight – ninth of the bees = 8/9 xx 2x^2 = (16x^2)/9

Number of bees in the lotus = 2

By the given condition

x + (16x^2)/9 + 2 = 2x2

9x + 16x2 + 18 = 18x ...(Multiply by 9)

18x2 – 16x2 – 9x – 18 = 0 ⇒ 2x2 – 9x – 18 = 0

2x2 – 12x + 3x – 18 = 0

2x(x – 6) + 3 (x – 6) = 0

(x – 6) (2x + 3) = 0

x – 6 = 0 or 2x + 3 = 0

x = 6 or 2x = – 3 ⇒ x = (-3)/2   ...(number of bees will not be negative)

Total number of black bees = 2x2 = 2(6)

= 72

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#### APPEARS IN

Samacheer Kalvi Mathematics Class 10 SSLC Tamil Nadu State Board
Chapter 3 Algebra
Exercise 3.12 | Q 6 | Page 116