Question 110
For real numbers a and b write $$a * b = a^2 + ab - b^2$$. If $$4 * x = 6$$ then $$(x - 2)^2 =$$
Solution
Given, $$a * b = a^2 + ab - b^2$$
$$4 * x = 6$$
$$\Rightarrow$$ $$4^2+4x-x^2=6$$
$$\Rightarrow$$ $$16+4x-x^2=6$$
$$\Rightarrow$$ $$x^2-4x-10=0$$
$$\Rightarrow$$ $$x^2-4x+4-14=0$$
$$\Rightarrow$$ $$\left(x-2\right)^2-14=0$$
$$\Rightarrow$$ $$\left(x-2\right)^2=14$$
Hence, the correct answer is Option C
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