To find the value of x²-5x+3 when x=15-√2, we substitute the value of x into the expression:
x² - 5x + 3 = (15-√2)² - 5(15-√2) + 3
First, let's expand (15-√2)² using the formula for the square of a binomial:
(15-√2)² = (15)² - 2(15)(√2) + (√2)²
= 225 - 30√2 + 2
Simplifying further:
(15-√2)² = 227 - 30√2
Now we substitute this back into the expression:
x² - 5x + 3 = 227 - 30√2 - 5(15-√2) + 3
= 227 - 30√2 - 75 + 5√2 + 3
= 155 - 25√2
Therefore, the value of x²-5x+3 when x=15-√2 is 155 - 25√2.