A binary operation ∆ is defined on the set R, of
real numbers by
𝑎 ∆ 𝑏 = 𝑎 + 𝑏√2. Find (2 ∆ − 3) ∆ 5
A. 2 + 5√2
B. 2 + 2√2
C. 2 − 3√2
D. −3 + 5√2
Firstly, we can use the definition of ∆ to find 2 ∆ − 3:
2 ∆ − 3 = 2 + (-3)√2 = 2 - 3√2
Next, we can use this result and the definition of ∆ to find (2 ∆ − 3) ∆ 5:
(2 ∆ − 3) ∆ 5 = (2 - 3√2) ∆ 5
= (2 - 3√2) + 5√2
= 2 + 2√2
Therefore, the answer is B. 2 + 2√2.
To find (2 ∆ −3) ∆ 5 using the binary operation ∆ on the set of real numbers, let's substitute the values into the expression step by step.
Step 1: Calculate 2 ∆ −3
Substitute a = 2 and b = -3 into the formula:
2 ∆ (-3) = 2 + (-3)√2
= 2 - 3√2
Step 2: Calculate (2 ∆ −3) ∆ 5
Substitute the result from step 1, 2 - 3√2, and b = 5 into the formula:
(2 - 3√2) ∆ 5 = (2 - 3√2) + 5√2
= 2 + 5√2 - 3√2
= 2 + 2√2
Therefore, (2 ∆ −3) ∆ 5 = 2 + 2√2, which is option B.