Answers
Answer:
Answer:
Possible values of x are - 4 , 2 , - 3 and 1.
Step-by-step explanation:
Given,
( x^2 + 2x )( x^2 + 2x - 11 ) + 24 = 0
Let : x^2 + 2x = a
Continued :
= > a( a - 11 ) + 24 = 0
= > a^2 - 11a + 24 = 0
= > a^2 - ( 8 + 3 )a + 24 = 0
= > a^2 - 8a - 3a + 24 = 0
= > a( a - 8 ) - 3( a - 8 ) = 0
= > ( a - 8 )( a - 3 ) = 0
= > a = 8 or 3
Case 1 : a = 8
= > x^2 + 2x = 8
= > x^2 + 2x - 8 = 0
= > x^2 + ( 4 - 2 )x - 8 = 0
= > x^2 + 4x - 2x - 8 = 0
= > x( x + 4 ) - 2( x + 4 ) = 0
= > ( x + 4 )( x - 2 ) = 0
= > x = - 4 or x = 2
Case 2 :
= > x^2 + 2x = 3
= > x^2 + 2x - 3 = 0
= > x^2 + ( 3 - 1 )x - 3 = 0
= > x^2 + 3x - x - 3 = 0
= > x( x + 3 ) - ( x + 3 ) = 0
= > ( x + 3 )( x - 1 ) = 0
= > x = - 3 or 1
Possible values of x are - 4 , 2 , - 3 and 1.
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Question :- Solve (x²+2x)(x² + 2x - 11) + 24 = 0 .
Solution :-
Let (x²+2x) = y .
Putting y in Question now, we get,
→ y² - 11y + 24 = 0
Splitting the Middle Term now,
→ y² - 8y - 3y + 24 = 0
→ y ( y - 8 ) - 3( y - 8) = 0
→ ( y - 8 ) ( y - 3 ) = 0
Putting Again Back y as (x² + 2x) now ,
→ ( x² + 2x - 8 ) ( x² + 2x - 3 ) = 0
Splitting the Middle term now,
→ ( x² + 4x - 2x - 8 ) ( x² + 3x - 1x - 3) = 0
→ [x(x + 4) -2(x + 4) ] [x(x + 3) - 1(x + 3)] = 0
→ [(x+4)(x-2)] * [(x+3)(x-1)] = 0
Now, putting All Equal to 0 , we get,
→ x + 4 = 0 , =>> x = (-4)
→ x - 2 = 0 , =>> x = 2
→ x + 3 = 0 , =>> x = (-3)
→ x - 1 = 0 , =>> x = 1
Hence, value of x will be (-4), 2 , (-3) and 1
ANSWER
Math4 minutes ago
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there are only rational number and no irrational no