For Q. 17 I believe it's "the function has a minimum at -1" take this answer with a grain of salt but the other three seem to be true and I don't know how to solve this one so I'm assuming it's the false one.

6 0

3 years ago

Item 6 for what value of a is 8x−8+3ax=5ax−2a an identity?

Readme [11.4K]

Let's rewrite the expression as

$8x+3ax-5ax = 8-2a \iff 8x - 2ax = 8-2a \iff 2x(4-a) = 2(4-a)$

So, if $a \neq 4$ , you may divide both sides by $4-a$ , the equation becomes $2x=2$ , and the only solution is $x=1$ , which means that this is not an identity (an indentity is tautologically true, no matter the value of x).

If instead $a = 4$ , you are multiplying both sides by zero, so the equation becomes

$2x \cdot 0 = 2 \cdot 0 \iff 0=0$

So, it doesn't matter which value for x you choose, because you will always end up with $0=0$ , which is obviously always true.

8 0

4 years ago