Question

what did the maidens do to make her cry
$23y + 72 {95}^{?} 2 \frac{?}{?} \times \frac{?}{?}$
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Answer 1

Answer:

Solve for p:

p^2 (-p^2 + h^2) = h^2 x^2

Expand out terms of the left hand side:

-p^4 + h^2 p^2 = h^2 x^2

Subtract h^2 x^2 from both sides:

h^2 p^2 - p^4 - h^2 x^2 = 0

Substitute y = p^2:

-h^2 x^2 + h^2 y - y^2 = 0

Multiply both sides by -1:

h^2 x^2 - h^2 y + y^2 = 0

Subtract h^2 x^2 from both sides:

y^2 - h^2 y = -h^2 x^2

Add h^4/4 to both sides:

y^2 - h^2 y + h^4/4 = -h^2 x^2 + h^4/4

Write the both sides as a square:

(y - h^2/2)^2 = 1/4 h^2 (-2 x + h) (2 x + h)

Take the square root of both sides:

y - h^2/2 = 1/2 sqrt(h^2 (-2 x + h) (2 x + h)) or y - h^2/2 = -1/2 sqrt(h^2 (-2 x + h) (2 x + h))

Add h^2/2 to both sides:

y = h^2/2 + 1/2 sqrt(h^2 (-2 x + h) (2 x + h)) or y - h^2/2 = -1/2 sqrt(h^2 (-2 x + h) (2 x + h))

Substitute back for y = p^2:

p^2 = h^2/2 + 1/2 sqrt(h^2 (-2 x + h) (2 x + h)) or y - h^2/2 = -1/2 sqrt(h^2 (-2 x + h) (2 x + h))

Take the square root of both sides:

p = sqrt(h^2/2 + 1/2 sqrt(h^2 (-2 x + h) (2 x + h))) or p = -sqrt(h^2/2 + 1/2 sqrt(h^2 (-2 x + h) (2 x + h))) or y - h^2/2 = -1/2 sqrt(h^2 (-2 x + h) (2 x + h))

h^2 (-2 x + h) (2 x + h) = -4 h^2 x^2 + h^4:

p = sqrt(h^2/2 + 1/2 sqrt(-4 h^2 x^2 + h^4)) or p = -sqrt(h^2/2 + 1/2 sqrt(h^2 (-2 x + h) (2 x + h))) or y - h^2/2 = -1/2 sqrt(h^2 (-2 x + h) (2 x + h))

h^2 (-2 x + h) (2 x + h) = -4 h^2 x^2 + h^4:

p = sqrt(h^2/2 + 1/2 sqrt(-4 h^2 x^2 + h^4)) or p = -sqrt(h^2/2 + 1/2 sqrt(-4 h^2 x^2 + h^4)) or y - h^2/2 = -1/2 sqrt(h^2 (-2 x + h) (2 x + h))

Add h^2/2 to both sides:

p = sqrt(h^2/2 + 1/2 sqrt(-4 h^2 x^2 + h^4)) or p = -sqrt(h^2/2 + 1/2 sqrt(-4 h^2 x^2 + h^4)) or y = h^2/2 - 1/2 sqrt(h^2 (-2 x + h) (2 x + h))

Substitute back for y = p^2:

p = sqrt(h^2/2 + 1/2 sqrt(-4 h^2 x^2 + h^4)) or p = -sqrt(h^2/2 + 1/2 sqrt(-4 h^2 x^2 + h^4)) or p^2 = h^2/2 - 1/2 sqrt(h^2 (-2 x + h) (2 x + h))

Take the square root of both sides:

p = sqrt(h^2/2 + 1/2 sqrt(-4 h^2 x^2 + h^4)) or p = -sqrt(h^2/2 + 1/2 sqrt(-4 h^2 x^2 + h^4)) or p = sqrt(h^2/2 - 1/2 sqrt(h^2 (-2 x + h) (2 x + h))) or p = -sqrt(h^2/2 - 1/2 sqrt(h^2 (-2 x + h) (2 x + h)))

h^2 (-2 x + h) (2 x + h) = -4 h^2 x^2 + h^4:

p = sqrt(h^2/2 + 1/2 sqrt(-4 h^2 x^2 + h^4)) or p = -sqrt(h^2/2 + 1/2 sqrt(-4 h^2 x^2 + h^4)) or p = sqrt(h^2/2 - 1/2 sqrt(-4 h^2 x^2 + h^4)) or p = -sqrt(h^2/2 - 1/2 sqrt(h^2 (-2 x + h) (2 x + h)))

h^2 (-2 x + h) (2 x + h) = -4 h^2 x^2 + h^4:

Answer: |

| p = sqrt(h^2/2 + 1/2 sqrt(-4 h^2 x^2 + h^4)) or p = -sqrt(h^2/2 + 1/2 sqrt(-4 h^2 x^2 + h^4)) or p = sqrt(h^2/2 - 1/2 sqrt(-4 h^2 x^2 + h^4)) or p = -sqrt(h^2/2 - 1/2 sqrt(-4 h^2 x^2 + h^4))

Hope it don't help u....xD