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Deductive Reasoning

Prove that if...

Question

Prove that if then each is equal to . Is this true for other numbers, instead of 2 and 5?

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Solution

We have

, i.e., the fractions are the different forms of the same number.

Let

⇒ x = = uz and y = = vz

_As _{, we get:}

Let us suppose we have numbers a and b, c and d instead of 2 and 5 in the given equation.

Therefore, we need to show

_As _{, we get:}

Hence, we can use any number instead of the numbers 2 and 5 for the given equation to hold true.

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Similar questions

Prove that if then . Will this be true if we use some other numbers instead of 2, 5, 4 and 6?

\frac{5 x + 6 y}{5 u + 6 y} = \frac{5 x - 6 y}{5 u - 6 y}

:
then prove that x: y = u: v

Q. Prove that the straight lines

x + 2 y + 1 = 0

2 x - y + 5 = 0

are perpendicular to each other.

\frac{u}{v} = \frac{w}{x} = \frac{y}{z}

then show that each ratio is equal to

{[\frac{u w^{2} + 7 u y^{2} + 3 y u^{2}}{u x^{2} + 7 x^{2} + 3 z v^{2}}]}^{\frac{1}{3}} .

\to u, \to v

\to w

| \to u | = 1, | \to v | = 2,

| \to w | = 3.

If the projection of

\to v

\to u

is equal to that

\to w

\to u

\to v

\to w

are perpendicular to each other, then |

\to u

\to v

\to w

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