the product of two consecutive positive integers is 306. we need to find the integers
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17 & 18
Step-by-step explanation:
let one number be x
so other will be (x+1)
product of both number = (x)(x+1)
=> 306 = x² + x
=> x² + x - 306 = 0
using , x = { -b ± √(b² -4ac) } ÷ 2a
=> x ={ (-1) ± √ ( 1² - (4)(1)(-306) ) } ÷ 2(1)
=> x = { -1 ± √ ( 1 + 1224) } ÷ 2
=> x = { -1 ± √ (1225) } ÷ 2
=> x = { -1 ± 35 } ÷ 2
=> x = (-1 + 35)/2 .......or ...... x = (-1-35)/2
=> x = 34/2 .......or x = -36/2
=> x = 17 ........or........ x = -18
as the number are positive integer
therefore ,
x = 17
x+1 = 18
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