What is the value of x? (20\ (35\ (60\ (70\
What is the value of x? (20\ (35\ (60\ (70\
The Correct Answer and Explanation is:
The expression you provided is: x=20 (35 (60 (70x = 20 \ (35 \ (60 \ (70
However, the expression seems to be incomplete or improperly formatted. It appears to be an attempt at expressing nested operations, but it lacks clarity about what operation is being performed — such as addition, subtraction, multiplication, division, or a function/operator such as GCD, LCM, or a custom notation (e.g., continued fractions or nested functions).
Let’s consider a common context for nested parentheses like this. One possibility is that it’s meant to represent nested function application. For example, if this represents nested greatest common divisors: x=gcd(20,gcd(35,gcd(60,70)))x = \gcd(20, \gcd(35, \gcd(60, 70)))
Then we compute it step-by-step:
- gcd(60,70)=10\gcd(60, 70) = 10
- gcd(35,10)=5\gcd(35, 10) = 5
- gcd(20,5)=5\gcd(20, 5) = 5
So, under this assumption, the value of x=5x = 5.
Explanation:
To determine the value of the expression 20 (35 (60 (7020\ (35\ (60\ (70, we must interpret the notation correctly. This format suggests nested operations with values wrapped in parentheses, implying a hierarchical or recursive evaluation. Since the specific operation is not stated, we infer it based on common mathematical practices. One such context is the greatest common divisor (GCD) — a widely used operation in number theory.
The GCD of two integers is the largest number that divides both without leaving a remainder. When GCD is nested like this: x=gcd(20,gcd(35,gcd(60,70)))x = \gcd(20, \gcd(35, \gcd(60, 70)))
we evaluate from the innermost pair outward:
- GCD(60, 70):
Both 60 and 70 are divisible by 10. So, gcd(60,70)=10\gcd(60, 70) = 10. - GCD(35, 10):
35 and 10 share a common factor of 5. Thus, gcd(35,10)=5\gcd(35, 10) = 5. - GCD(20, 5):
20 is divisible by 5. Therefore, gcd(20,5)=5\gcd(20, 5) = 5.
So, the final value of xx is 5.
This kind of nested GCD evaluation is helpful in simplifying numbers or algorithms like the Euclidean algorithm, where we find GCDs step-by-step. It’s important in areas like cryptography, computer science, and algorithm optimization.
Thus, assuming the operation is GCD, the correct and final value of x=5x = 5.
