Math, asked by abhisheku1132, 29 days ago

Write x²-5x+¹ in the form (X+a)²+b

Answers

Answered by keybytegamer1m
1

Answer:

Solution:

\begin{gathered}\\\end{gathered}

\begin{gathered}x^2 - 5x + 8 \\\\\end{gathered}

x

2

−5x+8

Form a set of (b/2)² into the expression:

\begin{gathered}x^2 - 5x + (\dfrac{5}{2})^2 - (\dfrac{5}{2})^2 + 8 \\\\\end{gathered}

x

2

−5x+(

2

5

)

2

−(

2

5

)

2

+8

Rewrite (a² - 2ab + b²) as (a - b)² in the expression:

\begin{gathered}\bigg(x - \dfrac{5}{2}\bigg)^2 - (\dfrac{5}{2})^2 + 8 \\\\\end{gathered}

(x−

2

5

)

2

−(

2

5

)

2

+8

Combine the terms outside the (a - b)² in the expression:

\bigg(x - \dfrac{5}{2}\bigg)^2 - \dfrac{25}{4} + 8(x−

2

5

)

2

4

25

+8

\begin{gathered}\bigg(x - \dfrac{5}{2}\bigg)^2 + \dfrac{7}{4} \\\\\end{gathered}

(x−

2

5

)

2

+

4

7

Matching the expression with (x - a)² + b:

a = \dfrac{5}{2}a=

2

5

\begin{gathered}b = \dfrac{7}{4} \\\\\end{gathered}

b=

4

7

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