Can you please help me solve this equation:

Question

16x^2+25y^2-400=0.

Answer 1

16x^2 + 25y^2 - 400 = 0.

Subtract (16x^2 - 400) from each side.

25y^2 = 400 - 16x^2

Divide each side by 25.

y^2 = (400 - 16x^2)/25

Extract square roots.

y = sqrt ((400 - 16x^2)/25)

f(x) = y = sqrt ((400 - 16x^2)/25).

Let

f(x) = y = sqrt ((400 - 16x^2)/25) = 0

Squaring on each side.

(400 - 16x^2)/25 = 0

Multiply 25 to each side.

400 - 16x^2 = 0

Add 16x^2 to each side.

400 = 16x^2

Divide each side by 16.

x^2 = 400/16 = 25

Extract square roots.

x = 5.

Solution of the function f(x) is 5.

Check :

Substitute x = 5 in y = sqrt ((400 - 16x^2)/25)4.

y = 0.

So,x = 5 is a solutionof the equation.

Answer 2

The Diophantine equation is 16x² + 25y² - 400 = 0

Diophantine equation form is Ax² + Bxy + Cy² +Dx + Ey + F = 0

A = 16, B = 0, C = 25, D = 0,E = 0, F = -400.

B² -4AC = 0-4(16)(25) = -400

B² - 4AC is less than zero.

So the equation is ellipse.

Since the ellipse is a closed figure,the number of solutions will be finite.

The value of x  should be between the the roots of this equation.

Compare it to quadratic form ax² + bx + c.

If x = 0 then 

Solution

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