Question

(64+36)^2-(64-36)^2/64*36​

Answer 1

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Answer 2

Answer:

Required answer is 4.

Step-by-step explanation:

Given,

$\frac{ {(64 + 36)}^{2} - {(64 - 36)}^{2} }{64 \times 36}$

Let,

$a = 64 \\ b = 36$

So,

$\frac{ {(a + b)}^{2} - {(a - b)}^{2} }{a \times b}$

We know,

${(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \\ {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab$

So,

$\frac{ {(a + b)}^{2} - {(a - b)}^{2} }{ab} \\ = \frac{ ({a}^{2} + {b}^{2} + 2ab) - ( {a}^{2} - 2ab + {b}^{2}) }{ab} \\ = \frac{ {a}^{2} + {b}^{2} + 2ab - {a}^{2} + 2ab - {b}^{2} }{ab} \\ = \frac{4ab}{ab} \\ = 4$

So,

$\frac{ {(64 + 36)}^{2} - {(64 - 36)}^{2} }{64 \times 36} = 4$

This is a problem of Power of indices.

Some important formulas of Power of indices,

${x}^{0} = 1 \\ {x}^{1} = x \\ {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ {x}^{ {y}^{a} } = {x}^{ya} \\ {x}^{ - 1} = \frac{1}{x} \\ {x}^{a} \times {y}^{a} = {(xy)}^{a}$

Power of indices related two more questions:

https://brainly.in/question/20611233

https://brainly.in/question/8929724

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