Solve the following by factorization method
4x² - 2(a² + b²)x + a²b² = 0
Answers
Equation: 4x² - 2(a² + b²)x + a²b²
So you know how to factorize ryt? First of all multiply 1st and last term :-)
→ 4x² × a²b²
→ 4x²a²b²
Now focus middle term, - 2(a² + b²)x
Let's unbox it, xD
→ - 2(a²x + b²x)
→ - 2a²x - 2b²x
Multiply both terms, (-2a²x • - 2b²x) = 4x²a²b².
Hence now let's start factorizing,
→ 4x² - 2a²x - 2b²x + a²b²
→ 2x(2x - a²) - b²(2x - a²)
→ (2x - a²)(2x - b²) = 0
Answer: x = a²/2 and b²/2
Answer:
x=a²/2 and x=b²/2
Step-by-step explanation:
To find --->Solve following equation by
------------ factorization method
4x²-2(a²+b²)x+a²b²=0,
Solution--->
-------------
4x²-2(a²+b²)x+a²b²=0
Multiplying x by 2(a²+b²) in middle term
=> 4x²-2(a²x+b²x)+ a²b² =0
Changing the sign of middle term
=> 4x²-2a²x-2b²x+a²b²=0
Taking 2x common from first two terms and (-b²) from last two terms
=> 2x(2x-a²)-b²(2x-a²)=0
Now taking (2x-a²) common
=> (2x-a²)(2x-b²)=0
If 2x-a²=0
=> 2x=a²
=> x=a²/2
If 2x-b²=0
=> 2x=b²
=> x=b²/2
So x=a²/2 or x=b²/2
Additional information--->
-------------------------------------
1) ax²+bx+c=0
Solution of quadertic equation is
-b ±√(b²-4ac)
x=-----------------------
2a
2) ax²+bx+c=0
If roots of equation is α and β then
α+β=-b/a
αβ=c/a
3) If roots of equation are α and β then equation is
x²-(sum of roots )x+(product of
roots)=0