the digit at tens place of atwo digit no is 2more than twice the digit at unit place if the product of digits is 24 find the two no
Answers
Hi.
Good Question and Keep Progressing.
Here is your answer---
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Let the digits at unit place be y and at tens place be x.
Thus, Number = 10x + y
According to the question,
x = 2 + 2y -------------------------eq(i)
Also, xy = 24 -----------------------------eq(ii)
Putting eq(i) in eq(ii),
(2 + 2y)y = 24
2y + 2y^2 - 24 = 0
2y^2 + 2y - 24 = 0
y^2 + y - 12 = 0
Splitting The middle Term,
y^2 + 4y - 3y - 12 = 0
y(y + 4) - 3(y + 4) = 0
(y+4)(y - 3) = 0
By Zero Product Rule,
y + 4 = 0 y - 3 =0
y = -4 y = 3
For y = -4 in eq(i),
x = 2 + 2( -4)
x = 2 - 8
x = -6
For, y=3 in eq(i)
x = 2 + 2(3)
x = 2 + 6
x = 8
For x = 8 and y= 3,
Number = 10(8) + 3
= 80 + 3
= 83
For x = -6 and y = -4
Number = 10(-6) + (-4)
= -60 -4
= -64
Thus, Two - digits number is 83 or -64.
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Hope it helps.