MCQ
જે વિધેય $f(x)=\frac{\sqrt{x^2-25}}{\left(4-x^2\right)}+\log _{10}\left(x^2+2 x-15\right)$ નો પ્રદેશ $(-\infty, \alpha) \cup[\beta, \infty)$ હોય, તો $\alpha^2+\beta^3=$___________.
- A$140$
- B$175$
- C$150$
- D$125$
$ \text { Domain : } x^2-25 \geq 0 \Rightarrow x \in(-\infty,-5] \cup[5, \infty) $
$ 4-x^2 \neq 0 \Rightarrow x \neq\{-2,2\} $
$ x^2+2 x-15>0 \Rightarrow(x+5)(x-3)>0 $
$ \Rightarrow x \in(-\infty,-5) \cup(3, \infty) $
$ \therefore x \in(-\infty,-5) \cup[5, \infty) $
$ \alpha=-5 ; \beta=5 $
$ \therefore \alpha^2+\beta^3=150$
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