Question

If $\bf \sqrt{m} + \sqrt{n} - \sqrt{p} = 0$ then find the value of m + n - p .

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Answer 1

Answer:

$\sf -2\sqrt{mn}$

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Step-by-step explanation:

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$\sf \dashrightarrow \ \sqrt{m} + \sqrt{n} - \sqrt{p} = 0$

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On transposing - √p to the right we get;

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$\sf \dashrightarrow \ \sqrt{m} + \sqrt{n} = \sqrt{p}$

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We're asked to find the value of m + n - p, so we'll need the terms "m", "n", and "p" in the equation we're currently operating on. In order to do so, we'll need to remove the roots, we can do that by squaring the equation on both sides.

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$\sf \dashrightarrow \ \Big\{\sqrt{m} + \sqrt{n} \Big\}^2 = \Big\{ \sqrt{p} \Big\}^2$

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On using the identity (a + b)² = a² + b² + 2ab we get;

[Where a = √m and b = √n]

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$\sf \dashrightarrow \ \Big\{\sqrt{m}\Big\}^2 + \Big\{\sqrt{n}\Big\}^2 + 2\Big\{\sqrt{m}\Big\}\Big\{\sqrt{n}\Big\} = \Big\{\sqrt{p}\Big\}^{2}$

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We know that [√a]² = √a × √a, on using this identity we get;

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$\sf \dashrightarrow \ \Big\{\sqrt{m} \ \times \sqrt{m}\Big\} + \Big\{\sqrt{n} \ \times \sqrt{n}\Big\} + 2\sqrt{mn} = \Big\{ \sqrt{p \times p}\Big\}$

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We know that √a × √a = √[a × a], on applying this we get;

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$\sf \dashrightarrow \ \Big\{\sqrt{m \times m}\Big\} + \Big\{\sqrt{n \times n}\Big\} + 2\sqrt{mn} = \Big\{ \sqrt{p \times p}\Big\}$

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We know that √[a × a] = √[a²], on applying this in the equation we get;

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$\sf \dashrightarrow \ \Big\{\sqrt{m^2}\Big\} + \Big\{\sqrt{n^2}\Big\} + 2\sqrt{mn} = \Big\{\sqrt{\sf p^2}\Big\}$

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The squares and the roots cancel each other, so we're left with;

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$\sf \dashrightarrow m + n + 2\sqrt{mn} = p$

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On transposing 'p' to the left we get;

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$\sf \dashrightarrow m + n + 2\sqrt{mn} - p = 0$

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On transposing '-2√(mn)' to the right we get;

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$\sf \dashrightarrow \textsf{\textbf{m + n - p = - 2}}\sqrt{\textsf{\textbf{mn}}}$

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Hence solved.

Answer 2

Answer:

Given:-

If √m + √n - √p = 0, then find the value of m + n - p.

To Find:-

The value of √m + √n - √p = 0.

Note:-

●》Here, for finding the value we need to transposed the term from its side to another and signs are also changed or not. For example - Positive becomes Negative ( signs are changed ), Negative becomes Positive ( signs are changed ).

●》When L.H.S side value and R.H.S side value are in root value then we need to square it for removing root.

Formula Used:-

■》( a + b )² = a² + b² + 2ab.

Solution:-

$\huge\red{√m + √n - √p = 0}$

$\huge\red{\ \ \ \ m + n - p = ?}$

☆ According to note first point~

▪︎$√m + √n - √p = 0$

▪︎$√m + √n = 0 + √p$

▪︎$√m + √n = √p$

☆ According to note second point~

▪︎$( √m + √n )²= ( √p )²$

☆ According to formula used~

▪︎$√m² + √n² + 2√mn = √p²$

☆ Root will be canceled by the square~

▪︎$m + n + 2√mn = p$

▪︎$m + n + 2√mn - p = 0$

▪︎$m + n - p = - 2√mn$

$\huge\pink{m + n - p = - 2√mn}$

Answer:-

Hence, the value of m + n - p is = - 2√mn

:)