x²-(x-2)² the sign will change or not why
Answers
Answer:
I hope its help you
Step-by-step explanation:
We will solve the equation
(x + 2)² = (x - 5)² + 7 …………………………………….(1)
for x in two different ways. In the First Method, we will use the formula for Difference of Two Squares. In the Second Method, we will use the formula for the Square of the Sum and Difference of Two Quantities.
First Method: a² - b² =(a+b)(a-b)
Transposing the first term on right-side to left-side,
(x + 2)² - (x - 5)² = 7
a = x+2, b = x-5 Therefore
(x + 2 + x - 5)(x+2-x+5) = 7
Or, (2x-3)7 = 7 Dividing both sides by 7,
2x - 3 = 1 Add +3 to both sides and obtain
2x = 4
This gives x = 2
Second Method: (a ± b)² = a² + b² ± 2ab
Use the above formulae to open the two brackets in (1).
On left-side, a = x and b = 2; on right-side, a = x and b = 5
x² + 4x + 4 = x² + 25 -10x + 7
Cancel the x² term on both sides. Bring all x terms to left-side and all the constant terms to right-side. We obtain
4x + 10x = 25 + 7 - 4 = 32 - 4
Or, 14x = 28 Dividing both sides by 14, we get
x = 28/14 = 2x14/14 = 2
Hence by both the methods, the solution of the given equation gives
x = 2 (Answer)
Verification:
Left-side = (x + 2)² = (2+2)² = 4² = 16
Right-side = (x - 5)² + 7 = (2–5)² + 7 = (-3)² + 7 = 9 + 7 = 16 = Left-side.
Verified That the solution of x = 2 is correct.
Answer:
x²-(x-2)²
by identity (a-b)² = a²+b²-2ab
= x²-x²+2²-2×x×2
= 4x - 4
= 4(x- 1)
so you can see here sign is change according to identity