(3x-1) (x^2-7x+11 = (1-2x)
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Answer:
1
What are all the possible solutions for x in (x²-7x+11) ^ (x²-3x-10) =1?
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Ragu Rajagopalan
Answered February 9, 2019
Given: (x2−7x+11)x2–3x−10=1
Possible cases:
Case-1: a0=1, if a≠0
⟹x2−3x−10=0⟹(x−5)(x+2)=0⟹x=5,−2
x2−7x+11≠0 when x=5 or x=−2
∴ solutions are : x=5,−2
Case-2: 1n=1
⟹x2−7x+11=1⟹x2−7x+10=0
⟹(x−5)(x−2)=0⟹x=5 or x=2
∴ solutions are : x=5,2
Case-3: (−1)2m=1
⟹x2−7x+11=−1⟹x2−7x+12=0
⟹(x−4)(x−3)=0⟹x=4 or x=3
Verify whether the power term (x2–3x−10) gives even values when x=4 or 3
When x=4:42−3(4)−10=16−12−10=−6⟹(−1)−6=1
When x=3:32−3(3)−10=9−9−10=−10⟹(−1)−10=1
Ans: x=±2,3,4,5
Akshay
Harsh Dwivedi
Answered December 15, 2019
⟹(x2–7x+11)(x2–3x−10)=(x2–7x+11)0
before solving lets consider some thing which is necessary before proceeding
a0=1,a≠0(01)
∴(x2–3x−10)=0
So,(x2–7x+11)≠0
⟹(x2–3x−10)=0(2)
⟹(x−5)(x+2)=0
From case 1 values of x be[+5,−2]
⟹(x2–7x+11)=1(3)
⟹x2–7x+10=0
⟹(x−5)(x−2)=0
Thus from case 2 possible values of x are,[+5,+2]
So possible values of x are[+5,+2,−2]■
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Aditya Karkare
Answered December 17, 2019
(x^2 -7x +11) ^ (x^2 -3x -10) = 1
The above expression is possible only when x^2 -3x +10 = 0 and x^2 -7x +11 = 1
x^2 -3x -10 = 0
10x^2 = -5x * 2x
-3x = -5x+2x
x^2 -3x -10 = 0
x^2 -5x +2x -10 = 0
x(x-5) +2(x-5) = 0
x+2= 0 and x-5= 0
x = -2 and x = 5
x^2 -7x +11 = 1
x^2 -7x +10 = 0
10x^2 = -5x * -2x
-7x = -5x -2x
x^2 -5x -2x+10 = 0
x(x-5) -2(x-5) = 0
x-2=0 and x-5=0
x=2 and x=5
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Answered February 9, 2019
Akshay
Ashutosh Sahu
Answered February 8, 2019
The solution is:-
Joyce Vedasundaram
Answered February 11, 2019
(x^2–7x+11)=1 OR (x^2–3x-10)=0
(x^2–7x+10)=0 OR (x^2–3x-10)=0
(x-5) =0 or (x-2)=0 OR (x-5)=0 or (x+2)=0
x=5 or x=2 or x=-2
Akshay
Kausik Roy
Answered February 10, 2019
2, -2, 3, 4, 5
Akshay