2(x-1/x)²-5(x+1/x+2)+18=0 please expalain step by step solution
Answers
Answer:
A triangle ABC is given .
The measurement of angle A = 70
The measurement of angle C = 140
Let the angle B be x
\implies\:70 \:+\: x\: = \:140⟹70+x=140 ( by exterior angle property )
\implies\:x \:= \:140\: -\: 70⟹x=140−70
\implies\:x \:= \:70⟹x=70
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⋆EXTERIOR ANGLE PROPERTY :- An exterior angle of a triangle is equal to the sum of the opposite interior angles.
⋆ANGLE SUM PROPERTY :- Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
⋆What are the types of triangle?
\implies⟹ An equilateral triangle has three equal sides and angles.
\implies⟹ An isosceles triangle can be drawn in many different ways. 2 sides and 2 angles are equal.
\implies⟹ A right-angled triangle has one 90° angle.
\implies⟹ A scalene triangle has three different angles and none of its sides are equal in length
Answer:
Step-by-step explanation:
Given : 1/(x−1)(x−2) +1/(x−2)(x−3) +1/(x−3)(x−4) = 1/6
[(x - 3) (x - 4) + (x - 1) (x - 4) + (x - 1) ( x - 2) ] / [(x - 1) (x - 2) (x - 3) (x - 4) ] = 1/6
[ By taking LCM]
[x² - 4x - 3x +12 + x² - 4x - 1x + 4 + x² - 2x - 1x +2] / [(x² - 5x + 4) (x² - 5x + 6] = ⅙
[3x² -7x - 5x -3x +18] / [(x² - 5x + 4) (x² - 5x + 6] = ⅙
[3x² - 15x +18] / [(x² - 5x + 4) (x² - 5x + 6] = ⅙
3[x² - 5x + 6] / [(x² - 5x + 4) (x² - 5x + 6] = ⅙
3/[(x² - 5x + 4) = ⅙
3 × 6 = (x² - 5x + 4)
18 = (x² - 5x + 4)
x² - 5x + 4 - 18 = 0
x² - 5x - 14 = 0
x² - 7x + 2x - 14 = 0
x(x - 7) + 2 (x - 7 ) = 0
(x + 2) (x - 7) = 0
(x + 2) = 0 or (x - 7) = 0
x = - 2 or x = 7