Question

If AAA+AA+A+A+A=10^n where A and n are single digits what is the value of A?​

Answer 1

Answer:

a3+a2+3a=10n  

i dont really know

Answer 2

Answer: Value of A = 8.

Step-by-step explanation:

The LHS of the question AAA+AA+A+A+A has to be expanded as AAA is a three digit number and AA is a two digit number.

Expansion of both terms using (face value)×(exponent of 10).

For example 222 is written as (200+20+2) as each digit has face value 2 and then multiply by exponent of 10:-2×$10^{2}$+2×10+2×1.

Similarly the LHS is divided into terms, So:-

AAA = 100×A+10×A+1×A.

AA=10×A+1×A and A=1×A.

Writing the LHS in this format:-

(100×A+10×A+1×A)+(10×A+1×A)+1×A+1×A+1×A (Taking A common and adding the terms).

Equals:- A×(100+10+1+10+1+1+1+1)= A×(111+11+3)=A×(125).

Now Equating the simplified LHS to RHS.

A×125=$10^n$,     (Taking the 125 to the RHS in denominator).

A=$10^n$/125.

As A is a integer value fractional values are not allowed for it,

So $10^n$ divides 125.    (125=5×5×5) which is 125=5³ and $10^n$=$2^n$×$5^n$

To do so $10^n$ must have 5³as factor so n has to be at least 3.

As both n and A are single digit integers we put n=3 and 4 to check for A.

1) at n=3, A=10³/125=1000/125=8.(Possible case).

2)at n=4, A=$10^4$/125=10000/125=80(Not possible as both are single digit integers but here A is double digit)

Hence,

Answer:-Value of A is equal to 8.

For more such questions:-https://brainly.in/question/15056322

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