Question

the product of two successive inregral multiple of 5 is 300 then the number​

Answer 1

Answer:

SOLUTION :

GIVEN :  The product of two successive integral multiples of 5 is 300.

Let the two successive integral multiples of 5  be 5x and 5(x+1)

A.T.Q  

5x × 5(x +1) = 300

5x (5x + 5) = 300

25x² + 25x - 300 = 0

25(x² + x - 12) = 0

x² + x - 12 = 0

x² + 4x - 3x -12 = 0

[By middle term splitting method]

x(x + 4) - 3(x + 4) = 0

(x + 4) (x - 3) = 0

(x + 4) = 0  or  (x - 3) = 0

x = - 4  or  x = 3  

CASE 1 :  

When x = - 4 , then first integer be  

5x = 5 (- 4) = -20

Second integer be  

5(x+1) = 5 (- 4  + 1) = 5 × - 3 = - 15

CASE : 2  

When x = 3 , then first integer be  

5x = 5 × 3 = 15

Second integer be  

5(x+1) = 5 (3 + 1) = 5 × 4 = 20  

Hence, the two successive integral multiples of 5 are (15, 20) and (-15 and -20).