Question

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Answer 1

Given Equation:-

• x² + 8x + 16

⠀

To find:-

• Value of x.

⠀

Solution:-

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{\tt{\bigstar{Concept{\bigstar}}}}$

Observe the expression; it has three terms. Therefore, it does not fit Identity III. Also, it's first and third terms are perfect squares with a positive sign before the middle term. So, it is of the form a² + 2ab + b² where a = x and b = 4.

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Such that,

$\tt\longrightarrow\: \: \: \: \: \:\: \: \: \: \: \:\: \: \: \: \: \:\: \: \: \: \: \:\: \: \: \: \: \:{a^2 + 2ab + b^2}$

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$\tt\longrightarrow\: \: \: \: \: \:\: \: \: \: \: \:\: \: \: \: \: \:{x^2 + 2 (x) (4) + 4^2}$

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$\tt\longrightarrow\: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \:{x^2 + 8x + 16}$

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Since,

$\tt\longrightarrow\: \: \: \: \: \: \: \: \: \: \: \:{a^2 + 2ab + b^2}$

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$\tt\longrightarrow\: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \:{(a + b)^2}$

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By comparison,

$\tt\longrightarrow\: \: \: \: \: \: \: \: \: \: \: \:{x^2 + 8x + 16}$

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$\tt\longrightarrow\: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \:{\boxed{\red{(x + 4)^2}}}$

Answer 2

Answer:

$Given Equation:-</p><p></p><p>x² + 8x + 16</p><p></p><p>⠀</p><p></p><p>To find:-</p><p></p><p>Value of x.</p><p></p><p>⠀</p><p></p><p>Solution:-</p><p></p><p>\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{\tt{\bigstar{Concept{\bigstar}}}}★Concept★</p><p></p><p>Observe the expression; it has three terms. Therefore, it does not fit Identity III. Also, it's first and third terms are perfect squares with a positive sign before the middle term. So, it is of the form a² + 2ab + b² where a = x and b = 4.</p><p></p><p>⠀</p><p></p><p>Such that,</p><p></p><p>\tt\longrightarrow\: \: \: \: \: \:\: \: \: \: \: \:\: \: \: \: \: \:\: \: \: \: \: \:\: \: \: \: \: \:{a^2 + 2ab + b^2}⟶a2+2ab+b2</p><p></p><p>⠀</p><p></p><p>\tt\longrightarrow\: \: \: \: \: \:\: \: \: \: \: \:\: \: \: \: \: \:{x^2 + 2 (x) (4) + 4^2}⟶x2+2(x)(4)+42</p><p></p><p>⠀</p><p></p><p>\tt\longrightarrow\: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \:{x^2 + 8x + 16}⟶x2+8x+16</p><p></p><p>⠀</p><p></p><p>Since,</p><p></p><p>\tt\longrightarrow\: \: \: \: \: \: \: \: \: \: \: \:{a^2 + 2ab + b^2}⟶a2+2ab+b2</p><p></p><p>$

Step-by-step explanation:

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