Solve the following equations by the method of factorization:
1. 7x^2 + 49 = 0
2. 2x^2 +1 = 0
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Answer:
7x+1
Step-by-step explanation:
1) To find the factor of the (1+7x)² + (49x²-1) we will solve the terms individually.
2) (1+7x)² + (49x²-1)
(1+7x)² + (7x+1)(7x-1) { By the Identity A²-B²= (A+B)(A-B) }(7x+1)(1+7x+7x-1) { taking out the common terms}(7x+1)(14x)
3) The factors of the (1+7x)² + (49x²-1) are 7x+1 and 14x.
(7x+1) and 14x are factors.
The equation : x2+7x−1=0 is of the form ax2+bx+c=0 where:
a=1,b=7,c=−1
The Discriminant is given by:
Δ=b2−4⋅a⋅c
=(7)2−(4⋅(1)⋅−1)
=49+4=53
The solutions are found using the formula
x=−b±√Δ2⋅a
x=−7±√532⋅1=−7±√532
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