Question

If x2 + x = 19, then what is the value of (x + 5)2 + [1/(x + 5)2 ]?

Answer 1

Answer:

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Answer 2

The value of required expression is 79.

Step-by-step explanation:

Consider the provided information.

Let (x+5) = a then x = a-5

Substitute the value of x in $x^2 + x = 19$.

$(a-5)^2 + a-5 = 19$

$a^2+25-10a + a-5-19 =0$

$a^2-9a+1 =0$

$a^2-9a+1 =0$

$a^2+1 =9a$

$\frac{a^2+1}{a} =9$

Simplify $\frac{a^2+1}{a} =9$

$a+\frac{1}{a} =9$

Squaring both sides.

$a^2+\frac{1}{a^2}+2\times a \times\frac{1}{a} =81$

$a^2+\frac{1}{a^2}+2=81$

$a^2+\frac{1}{a^2}=79$

Substitute the value of a = x+5.

$(x + 5)^2 + \frac{1}{(x + 5)^2} =79$

Hence, the value of required expression is 79.

#Learn more

Find the value of k such that the quadratic polynomial x2-(k+6)+2(2k+1) has sum of the zeros is half of their product.

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