289x²+170x+24-38y-361y²
Answers
Answer:
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Answer :
Hint:
Here, we will rewrite the middle term and factorize the equation to get one linear equation and one quadratic equation. We will first solve the linear equation to find one of the roots of the given equation. Then we will solve the quadratic equation using the quadratic formula to get the required roots of the solution.
Formula Used:
Quadratic roots is given by the formula x=−b±b2−4ac−−−−−−−√2a
x=−b±b2−4ac2a
Complete step by step solution:
We are given an equation 28x3−9x2+1=0
28x3−9x2+1=0
Now, we will rewrite the middle term of the equation.
⇒28x3−16x2+7x2+1=0
⇒28x3−16x2+7x2+1=0
Now, we will add and subtract 4x
4x
on the left hand side, we get
⇒28x3−16x2+7x2+4x−4x+1=0
⇒28x3−16x2+7x2+4x−4x+1=0
Now, by rearranging the equation, we get
⇒28x3−16x2+4x+7x2−4x+1=0
⇒28x3−16x2+4x+7x2−4x+1=0
Now, by factoring the equation, we get
⇒4x(7x2−4x+1)+1(7x2−4x+1)=0
⇒4x(7x2−4x+1)+1(7x2−4x+1)=0
Again factoring out common terms, we get
⇒(4x+1)(7x2−4x+1)=0
⇒(4x+1)(7x2−4x+1)=0
Now applying zero product property, we get
⇒(4x+1)=0
⇒(4x+1)=0
or (7x2−4x+1)=0
(7x2−4x+1)=0
Now, we consider (4x+1)=0
(4x+1)=0
Subtracting 1 from both sides, we get
⇒4x=−1
⇒4x=−1
Dividing both sides by 4, we get
⇒x=−14
⇒x=−14
Now, we will consider (7x2−4x+1)=0
(7x2−4x+1)=0
Comparing the above equation with the general quadratic equation ax2+bx+c=0
ax2+bx+c=0
, we get
By substituting a=7,b=−4
a=7,b=−4
and c=1
c=1
in the formula ⇒x=−b±b2−4ac−−−−−−−√2a
⇒x=−b±b2−4ac2a
, we get
x=−(−4)±(−4)2−4(7)