Question

x=2 +√3 and x+y =4 ,then find the simplest value of xy+(1/xy)​

Answer 1

Question:

x=2 +√3 and x+y =4 ,then find the simplest value of xy+(1/xy)

Solution:

x=2 +√3 ⁣        ⁣   (1)          

x+y=4⁣           ⁣     (Given)

y=4-x

y=4-(2+√2)

y=4-2-√2

y=2-√2

therefore,

• x=2 +√3 and y=2-√2

putting the value of x and y in the equation xy+(1/xy)

⁣           

⁣           ${\boxed{\sf{\red{(a+b)(a-b)=a²-b²}}}}$

⁣          

$\bold{(2 +√3)(2-√2)+{\dfrac{1}{(2 +√3)(2-√2)}}}$

=⁣    $\bold{2²-(√2)²+{\dfrac{1}{2²-(√2)²}}}$

=⁣        $\bold{4-2+{\dfrac{1}{4-2}}}$

=⁣         $\bold{2+{\dfrac{1}{2}}}$

=⁣         $\bold{{\dfrac{4+1}{2}}}$

⁣ =         $\bold{{\dfrac{5}{2}}}$

╚════════════════════════╝

For More Information

(a+b)²=a² + b² + 2ab

(a-b)²=a² + b² -2ab

(a+b)(a-b)= a²-b²

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca.

Answer 2

Solution:

x=2 +√3 ⁣        ⁣   (1)          

x+y=4⁣           ⁣     (Given)

y=4-x

y=4-(2+√2)

y=4-2-√2

y=2-√2

therefore,

x=2 +√3 and y=2-√2

putting the value of x and y in the equation xy+(1/xy)

⁣           

refer the attachment file