Math, asked by pathakrenu70, 1 day ago

If () + ( − ) = + for all real , find ()​

Answers

Answered by SugaryHeart
3

Step-by-step explanation:

First let us find the range where Min (-(x – 1)2 + 2, (x – 2)2 + 1) is – (x – 1)2 + 2.

In other words, in which range is – (x – 1)2 + 2 < (x – 2)2 + 1.

–(x2 – 2x +1) + 2 < x2 – 4x + 4 + 1

0 < 2x2 – 6x + 4

x2 – 3x + 2 > 0

(x – 1) (x – 2) > 0

=> x > 2 or x < 1

Answered by crankybirds30
2

First let us find the range where Min (-(x – 1)2 + 2, (x – 2)2 + 1) is – (x – 1)2 + 2.

In other words, in which range is – (x – 1)2 + 2 < (x – 2)2 + 1.

–(x2 – 2x +1) + 2 < x2 – 4x + 4 + 1

0 < 2x2 – 6x + 4

x2 – 3x + 2 > 0

(x – 1) (x – 2) > 0

=> x > 2 or x < 1

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