Question

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Suppose x and y are real numbers and

[x + √(1 + x2)][y + √(1 + y2)] = 1

What is the value of:

(x + y)2




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Answer 1

Answer:

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Combustion is a chemical process or a reaction between Fuel (Hydrocarbon) and Oxygen. When fuel and oxygen react it releases the heat and light energy. Heat and light energy then result in the flame. So, the formula for Combustion reaction is Hydrobcarbon + Oxygen = Heat energy. Combustion is used in car motors and rocket engines and many other machineries.

Combustion is a chemical process where any fuel has a reaction with air (oxidant) to produce heat energy.And when this heat energy release it will also produce light in the form of a flame. This is the visible part of the reaction, the flames. The general exothermic reaction of combustion can be expressed as:

Hydrocarbon + Oxygen → Carbon Dioxide + Water + Heat Energy

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Answer 2

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Let us solve for y in terms of x.

Suppose:

u = x + v(1+ x2)

Then we can solve for y:

u(y + V(1+ y2)) = 1

y + v(1+ y2) = 1/u

V(1 + y2) = 1/u - y

1 + y2 = (1/u – y)2

1+ y2 = 1/u2 – 2y/u + y2 =

1 = 1/2 - 2y/u

2y/u = 1/2-1

y = (1/u – u)/2

Now let's determine the value of 1/

u.

u = x + v(1+ x2)

1/u = 1/(x + V (1 + x2))

We can multiply the numerator and denominator by the conjugate to get:

1/u = (x – v(1 + x2))/[(x + v1 + x2)(x - V(1+ =

x2))]

1/u = (x - V(1+ x2))/(x2 – (1+ x2) =

1/u = (x – v(1+ x2))/(-1) =

1/u = -x + v(1+ x2)

Thus we have:

y = (1/u – u)/2

y = (-x + v1 + x2) – (x + (1 + x2)/2

y = (-2x)/2

y = -x

And now we can easily solve the problem:

(x + y)2

=x - x)2 =

= 0