in a two digit number the tens digit is bigger the product of the digits is 27 and the difference between the two digits is 6 find the number
Answers
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let two digits be a and b
a×b=27 .....eq1
a=27÷b .....eq2
a-b=6 .....eq3
put eq2 in above equation
27÷b-b=6
(27-b2)÷b=6 #b2 is b square
27-b2=6b
b2+6b-27=0
solving simultaneous equation
b2+9b-3b-27=0
b(b+9)-3(b+9)
(b-3)(b+9)
b=3.....eq4
putting eq4 in eq3
a-b=6
a-3=6
a=6+3
a=9
Now the no. containing digits a and b= 93
hope u understand!!!
Answer:
Step-by-step explanation:
Given :-
The difference between two digits is 6 and the ten's digit is bigger than the unit's digit.
To Find :-
The Number
Solution :-
Let the unit's digit be x
Let ten's digit be (x + 6).
According to Question
⇒ x(x + 6) = 27
⇒ x² + 6x − 27 = 0
⇒ x² + 9x − 3x − 27 = 0
⇒ x(x + 9) − 3(x + 9) = 0
⇒ (x + 9) (x − 3) = 0
⇒ x = −9, 3
Since, the digits of a number cannot be negative.
So, x = 3.
Unit's digit = 3
Ten's digit = 9
Hence, the number is 93.