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Answer=-7(1+80√3)

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Answer 1

ANSWER

-7(1+80√3)

Step By Step Explanation

We have >

x =$\dfrac{1}{7+4\sqrt 3}$

Now on multiplying by ${7- 4\sqrt 3}$ In both numerator and denominator we get =>

x =$\dfrac{ 7-4\sqrt3 } {(7 + 4\sqrt 3)(7 - \sqrt 3)}$

{By using a² - b² = (a+b)(a-b)}

=> x =$\dfrac{ 7-4\sqrt3 } {49 - 48}$

=> x = ${ 7-4\sqrt3 }$

Now, again we have >

y = $\dfrac{1}{7 - 4\sqrt 3}$

So, on multiplying by ${7 + 4\sqrt 3}$ on both numerator and denominator we get >

=>y =$\dfrac{ 7+4\sqrt3 } {(7 + 4\sqrt 3)(7 - \sqrt 3)}$

{By using a² - b² = (a+b)(a-b)}

=> y =$\dfrac{ 7+4\sqrt3 } {49-48}$

=> Y = ${ 7+4\sqrt3}$

Now the given equation we have is

=>5x² - 7xy - 5y²

=>5(7-4√3)² - 7(7-4√3)(7+4√3) - 5(7+4√3)²

=> 5(49 + 48 - 56√3) -7(1) - 5(49 + 48 + 56√3)

=> 245 + 240 - 280√3 -7 - 245 - 240 - 280√3

=> -280√3 - 280√3 - 7

=> -560√3 - 7

=> -7(80√3 +1)

Remember

1)a² - b² = (a+b)(a-b)

2) (a+b)² = a² + b² + 2ab