Question

if x=2+√3,y=2-√3 let us calculate (ii)y²+1/y²​

Answer 1

Answer:

$5 - 3 root 3$

Step-by-step explanation:

2- root 3 whole

Answer 2

Step-by-step explanation:

QUESTION:

If x=2+√3, y=2-√3 let us calculate (y²+1/y²)

SOLUTION:

✅ y = 2-√3

✅ $\frac{1}{y} \\ = \frac{1}{2 - \sqrt{3} } \\ = \frac{1}{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } \\ = \frac{2 + \sqrt{3} }{4 - 3} \\ = 2 + \sqrt{3}$

$∴ ({y})^{2} + ({ \frac{1}{y} })^{2} \\ = {(2 - \sqrt{3}) }^{2} + {(2 + \sqrt{3}) }^{2} \\ = ({(2)}^{2} - 2 \times 2 \times \sqrt{3} + {( \sqrt{3}) }^{2} ) + ({(2)}^{2} + 2 \times 2 \times \sqrt{3} + {( \sqrt{3}) }^{2}) \\ = (4 - 4 \sqrt{3} + 3) + (4 + 4 \sqrt{3} + 3 ) \\ = 7 - 4 \sqrt{3} + 7 + 4 \sqrt{3} \\ = 14$