Question

If 3x-4y = 10 and xy = - 1 find 9x square + 16y square

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Answer 1

Answer:

Click on the picture

Step-by-step explanation:

Hope it will help

Answer 2

3x - 4y = 10 and xy = -1

y = -1/x from 2nd equation.

Substitute into the first.

3x - 4(-1/x) = 10

3x + 4/x = 10

multiply through by x

3x2 + 4 = 10x

3x2 - 10x + 4 = 0

Using quadratic equation solve for x:

x = [10 ±√[(-10)2-4(3)(4)]]/(2(3))

x = [10 ±√52]/6

x = (10 ±2√13)/6

x = (5 ±√13)/3

y = -1/x so:

For x = (5+√13)/3

y = -3/(5+√13)

For x = (5-√13)/3

y = -3/(5-√13)

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9x2 + 16y2

9[(5+√13)/3]2 + 16[-3/(5+√13)]2

= 9[(38+10√13)/9] + 16[9/(38+10√13)

= 38 + 10√13 + 144/(38+10√13)

= 76

Now try doing the same with

x = (5-√13)/3

y = -3/(5-√13)