The solution of the equation _7 _5 ( x^2 + 5 + x ) = 0 - Vidyadip

MCQ

The solution of the equation ${\log _7}{\log _5}$ $(\sqrt {{x^2} + 5 + x} ) = 0$

A
$x = 2$
B
$x = 3$
✓
$x = 4$
D
$x = - 2$

✓

Answer

Correct option: C.

$x = 4$

c
(c) ${\log _7}{\log _5}(\sqrt {{x^2} + 5 + x} ) = 0 = {\log _7}1$

$ \Rightarrow $ ${({x^2} + 5 + x)^{1/2}} = 5$

$ \Rightarrow $ $({x^2} + x + 5) = 25$$ \Rightarrow $ ${x^2} + x - 20 = 0$

$ \Rightarrow $ $ (x - 4)\,(x + 5) = 0$ $ \Rightarrow $ $ x = \,4,\, - 5$ ==> $x = 4$.

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