If 7272 can be written as 𝑎𝑏×𝑏𝑎a b ×b a , then find the values of 𝑎a and 𝑏b.𝑎=1,𝑏=3a=1,b=3𝑎=2,𝑏=3a=2,b=3𝑎=1,𝑏=2a=1,b=2𝑎=5,𝑏=2a=5,b=2
Question
If 7272 can be written as 𝑎𝑏 × 𝑏𝑎, then find the values of 𝑎 and 𝑏.
- 𝑎 = 1, 𝑏 = 3
- 𝑎 = 2, 𝑏 = 3
- 𝑎 = 1, 𝑏 = 2
- 𝑎 = 5, 𝑏 = 2
Solution
1. Break Down the Problem
We need to express the number 7272 in the form of , where and are digits. The digits form two two-digit numbers: (which represents ) and (which represents ).
2. Relevant Concepts
The expression can be expanded as: We need to determine and such that:
3. Analysis and Detail
Let's denote:
Multiply these two expressions:
Thus, we need to solve: Calculating gives an approximate range for and since the product is supposed to be around this number.
Step 4: Calculate Possible and
To find valid combinations of and , we can systematically check the options provided:
-
Option 1:
- (not valid)
-
Option 2:
- (not valid)
-
Option 3:
- (not valid)
-
Option 4:
- (not valid)
After checking these combinations, we realize none of the combinations yields 7272 as the result.
5. Verify and Summarize
Upon checking, we find that no provided combinations of and correctly reconstruct the number 7272 through the multiplicative expression .
Final Answer
There are no valid values of and among the provided options that satisfy . Each combination was validated, yielding different products.
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