the sum of digits of a two digit number is 12. the number is 6 times the unit digit find the number.
Answers
Answer:
Coefficient of x⁶y³ is 672.
Step-by-step explanation:
General term of expansion (a+b)ⁿ is
\bf \: T_{r+1} = \: \: ^nC_r \: \: \large \frak{ a ^{n−r} b ^r}T
r+1
=
n
C
r
a
n−r
b
r
For (x+2y)⁹,
Putting n =9, a=x, b=2y
\begin{gathered} \bf \: T_{r+1} = \: \: ^{9} C_r (x) ^{9−r} (2y) ^r \\ \\ \bf \: T _{r+1} = \: \: ^{9} C_r (x) ^{9−r} .(y) ^r .(2) ^r\end{gathered}
T
r+1
=
9
C
r
(x)
9−r
(2y)
r
T
r+1
=
9
C
r
(x)
9−r
.(y)
r
.(2)
r
Comparing with x⁶ y³ , we get, r = 3
Therefore,
\begin{gathered} \bf \: T _{r+1} \\ \: \tt ^9C_3 (x)^9−3 .y³ .2³ \\ \tt\: \: 9! (2)³× x⁶ × y³) / (3!.6!) \\ \: \tt 672x⁶ y³\end{gathered}
T
r+1
9
C
3
(x)
9
−3.y³.2³
9!(2)³×x⁶×y³)/(3!.6!)
672x⁶y³
Answer:
48
Step-by-step explanation:
Let assume number at tens place = x
And number at units place = y
So number = 10x + y
Given that sum of two digits is 12
=> x + y = 12
=> y = 12 – x ------ (1)
Also given number is 6 times the unit digit
=> 10x + y = 6y
=> 10x – 5y = 0
=> 2x – y = 0 ------- (2)
Substituting value of x from equation (1) in equation (2) we get
=>2x –( 12 – x) = 0
=> 3x = 12
=>x = 4
From (2) y = 12 – x = 12 - 4 = 8
Hence required number is 10 x 4 + 8 = 48