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If x is equals to root a 2b root a-2b upon root a 2b-root a-2b, prove that bx square - ax b =0?
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If x is equals to root a 2b root a-2b upon root a 2b-root a-2b, prove...
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If x is equals to root a 2b root a-2b upon root a 2b-root a-2b, prove...
Given:
x = √(a+2b) / √(a-2b)
To prove:
bx^2 - ax - b = 0
Proof:
Step 1: Simplify the given expression for x
x = (√(a+2b) / √(a-2b)) * (√(a+2b) / √(a+2b))
x = (a+2b) / (√(a-2b) * √(a+2b))
Step 2: Square the expression for x
x^2 = [(a+2b) / (√(a-2b) * √(a+2b))]^2
x^2 = (a+2b)^2 / ((√(a-2b))^2 * (√(a+2b))^2)
x^2 = (a+2b)^2 / ((a-2b) * (a+2b))
x^2 = (a+2b)^2 / (a^2 - (2b)^2)
x^2 = (a+2b)^2 / (a^2 - 4b^2)
Step 3: Simplify the denominator
x^2 = (a+2b)^2 / ((a+2b)(a-2b))
x^2 = (a+2b) / (a-2b)
Step 4: Substitute the value of x from the given expression
(a+2b) / (a-2b) = √(a+2b) / √(a-2b)
(a+2b)^2 = (√(a+2b))^2 * (a-2b)
(a+2b)^2 = (a+2b)(a-2b)
Step 5: Simplify the equation
a^2 + 4ab + 4b^2 = a^2 - 4b^2
4ab + 4b^2 = -4b^2
4ab = -8b^2
Step 6: Divide by 4b
a = -2b
Step 7: Substitute the value of a in the equation bx^2 - ax - b = 0
bx^2 - ax - b = b(a+2b) - (-2b)x - b
bx^2 - ax - b = ba + 2b^2 + 2bx - b
bx^2 - ax - b = ba + 2b^2 - 2bx - b
bx^2 - ax - b = 2b^2 + ba - 2bx - b
bx^2 - ax - b = 2b(b + a) - b(2x + 1)
bx^2 - ax - b = 2b(b + a - (2x + 1))
Step 8: Substitute the value of a = -2b
bx^2 - ax - b = 2b(b - 2b - (2x +
x = √(a+2b) / √(a-2b)
To prove:
bx^2 - ax - b = 0
Proof:
Step 1: Simplify the given expression for x
x = (√(a+2b) / √(a-2b)) * (√(a+2b) / √(a+2b))
x = (a+2b) / (√(a-2b) * √(a+2b))
Step 2: Square the expression for x
x^2 = [(a+2b) / (√(a-2b) * √(a+2b))]^2
x^2 = (a+2b)^2 / ((√(a-2b))^2 * (√(a+2b))^2)
x^2 = (a+2b)^2 / ((a-2b) * (a+2b))
x^2 = (a+2b)^2 / (a^2 - (2b)^2)
x^2 = (a+2b)^2 / (a^2 - 4b^2)
Step 3: Simplify the denominator
x^2 = (a+2b)^2 / ((a+2b)(a-2b))
x^2 = (a+2b) / (a-2b)
Step 4: Substitute the value of x from the given expression
(a+2b) / (a-2b) = √(a+2b) / √(a-2b)
(a+2b)^2 = (√(a+2b))^2 * (a-2b)
(a+2b)^2 = (a+2b)(a-2b)
Step 5: Simplify the equation
a^2 + 4ab + 4b^2 = a^2 - 4b^2
4ab + 4b^2 = -4b^2
4ab = -8b^2
Step 6: Divide by 4b
a = -2b
Step 7: Substitute the value of a in the equation bx^2 - ax - b = 0
bx^2 - ax - b = b(a+2b) - (-2b)x - b
bx^2 - ax - b = ba + 2b^2 + 2bx - b
bx^2 - ax - b = ba + 2b^2 - 2bx - b
bx^2 - ax - b = 2b^2 + ba - 2bx - b
bx^2 - ax - b = 2b(b + a) - b(2x + 1)
bx^2 - ax - b = 2b(b + a - (2x + 1))
Step 8: Substitute the value of a = -2b
bx^2 - ax - b = 2b(b - 2b - (2x +
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If x is equals to root a 2b root a-2b upon root a 2b-root a-2b, prove that bx square - ax b =0?
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If x is equals to root a 2b root a-2b upon root a 2b-root a-2b, prove that bx square - ax b =0? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If x is equals to root a 2b root a-2b upon root a 2b-root a-2b, prove that bx square - ax b =0? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x is equals to root a 2b root a-2b upon root a 2b-root a-2b, prove that bx square - ax b =0?.
If x is equals to root a 2b root a-2b upon root a 2b-root a-2b, prove that bx square - ax b =0? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If x is equals to root a 2b root a-2b upon root a 2b-root a-2b, prove that bx square - ax b =0? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x is equals to root a 2b root a-2b upon root a 2b-root a-2b, prove that bx square - ax b =0?.
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