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777dan777 [17]
3 years ago
9

Rewrite x2 − 6x + 7 = 0 in the form (x − a)2 = b, where a and b are integers, to determine the a and b values.

Mathematics
1 answer:
Setler79 [48]3 years ago
4 0

Answer:

Therefore values of a and b are

a=3\ and\ b = 2

Step-by-step explanation:

Rewrite x^{2}-6x+7=0 in the form

(x-a)^{2}=b

where a and b are integers,

To Find:

a = ?

b = ?

Solution:

x^{2}-6x+7=0 ..............Given

Which can be written as

x^{2}-6x=-7

(\frac{1}{2} coefficient\ of\ x)^{2}=(\frac{1}{2}\times -6)^{2}=9

Adding half coefficient of X square on both the side we get

x^{2}-6x+9=-7+9=2 ...................( 1 )

By identity we have (A - B)² =A² - 2AB + B²

Therefore,

x^{2}-6x+9=x^{2}-2\times 3\times x+3^{2}=(x-3)^{2}

Substituting in equation 1 we get

(x-3)^{2}=2

Which is in the form of

(x-a)^{2}=b

On comparing we get

a = 3 and b = 2

Therefore values of a and b are

a=3\ and\ b = 2

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