Question

Self Check? Solve: _aa_ 225 + 34a2-0. (Enter your answers from smallest to largest.)

Answer 1

Answers: (From smallest to the larget values)

$a=-5$   

$a=-3$

$a=+3$

$a=+5$

Explanation: The given equation is

$-a^4-225+34a^2=0$

multiplying by - sign on both sides

$a^4+225-34a^2=0$ ------------------------------------- (1)

Now, let us substitute a²=x . so, a⁴=x². So, equaation 1 becomes

$x^2+225-34x=0$

$x^2-34x+225=0$

This equation can be solved by factoring the middle term. There are two numbers -9 and -25 such that (-9)*(-25)=225 (product of first and last term) and -9-25=-34 (middle term). So,

$x^2-25x-9x+225=0$

$x(x-25)-9(x-25)=0$   

$(x-25)(x-9)=0$ ---------------------------------------------- (2)

So, we have

$(x-25)=0\Rightarrow x-25+25=0+25\Rightarrow x=25$ ---------------------------- (3)

$(x-9)=0\Rightarrow x-9+9=0+9\Rightarrow x=9$ ---------------------------------- (4)

Now, since a²=x. So,

(1) using x=25 in a²=x

$a^2=25$

taking square root on both sides

$\sqrt{a^2}=\sqrt{25}$

$a=\pm 5$

So, $a=+5$ and $a=-5$

(2) Using x=9 in a²=x

$a^2=9$

taking square root on both sides

$\sqrt{a^2}=\sqrt{9}$

$a=\pm3$   

So, $a=+3$ and $a=-3$

For checking substiture the values of a=+3, -3, +5 and -5 one by one and check the validity of eqn 1.