The product 18

The product of two consecutive natural numbers which are multiples of 3 is equal to 810. Find the two numbers.

Correct answer:

a =  27
b =  30

Step-by-step explanation:

a⋅ b=810 a=3A b=3B = 3⋅ (A+1)  3A⋅ 3⋅ (A+1)=810  3A⋅ 3⋅ (A+1)=810 9A2+9A−810=0 9=32 810=2⋅34⋅5 GCD(9,9,810)=32=9  A2+A−90=0  a=1;b=1;c=−90 D=b2−4ac=12−4⋅1⋅(−90)=361 D>0  A1,2​=2a−b±D​​=2−1±361​​ A1,2​=2−1±19​ A1,2​=−0.5±9.5 A1​=9 A2​=−10 A=A1​=9  a=3⋅ A=3⋅ 9=27

Our quadratic equation calculator calculates it.

b=3⋅ (A+1)=3⋅ (9+1)=30   Verifying Solution:  p=a⋅ b=27⋅ 30=810

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Showing 1 comment:
Dr. Math
3x(3x + 3) = 810
9x² + 9x - 810 = 0
x² + x - 90 = 0
(x + 10)(x - 9) = 0
x = -10 or x = 9
-10 is not natural no
x = 9
3x = 27, 3x + 3 = 30
Ans : 27 & 30





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