If a= 3 +2 root 2 , then find the value of a^2 - 1/a^2 ????
a = 3+2√2
a^2 = 9 + 12√2 + 8 = 17+12√2
1/a^2 = (17-12√2)/(289-288) = 17-12√2
a^2 + 1/a^2 = 34
sorry I didn't see the minus sign. But it's easy to fix. What do you get?
To find the value of a² - 1/a², we need to substitute the given value of "a" into the expression and then perform the calculations.
Given that a = 3 + 2√2, we can substitute it into the expression:
a² - 1/a² = (3 + 2√2)² - 1/(3 + 2√2)²
Now, let's simplify both terms separately:
- Simplifying the square of (3 + 2√2)²:
(3 + 2√2)² = (3 + 2√2)(3 + 2√2)
= 3(3) + 3(2√2) + 2√2(3) + 2√2(2√2)
= 9 + 6√2 + 6√2 + 4(2)
= 9 + 12√2 + 8
= 26 + 12√2
- Simplifying the term 1/(3 + 2√2)²:
1/(3 + 2√2)² = 1/(3 + 2√2)(3 + 2√2)
= 1/(9 + 12√2 + 8)
= 1/(17 + 12√2)
Now that we have simplified both terms, we can substitute them back into the expression:
a² - 1/a² = (3 + 2√2)² - 1/(3 + 2√2)²
= (26 + 12√2) - 1/(17 + 12√2)
Please note that the expression cannot be further simplified without rationalizing the denominator of the term 1/(17 + 12√2).