solve the following quadratic equations. Leave surds in your answers.
a) (x-3)^2-3=0
b) (3x-7)^2 =8
2a) x^4-5x^2+4=0
b) x-8=2squareroot x
a)
Add to both sides:
Add like terms:
Take the square root for both sides:
Add to both sides:
The solutions are and
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b)
Take the square root for both sides:
Add to both sides:
Divide both sides by :
Simplify the expression as :
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2a)
Find two numbers whose product is "the third term" and have the sum of "coefficient of the second term":
The numbers are and , such that and
Now factor the expression:
Using Zero-Product Property, it follows that:
or
Take the first equation:
Add to both sides:
Take the square root for both sides:
Take the second equation:
Add to both sides:
Take the square root for both sides:
Therefore, the solutions are
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b)
Square both sides:
Expand the square of the binomial on the left-hand side:
Square the right-hand side:
Subtract from both sides:
Add like terms:
Write as a difference:
Factor out from the first two expressions:
Factor out from the second two expressions:
Factor out from the expression:
Using Zero-Product Property, it follows that:
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