Let x, y, z be variables such that (x + y + z) = k, where k is a constant. If (x + z - y) × (x - z + y) is proportional to yz, then (y + z - x) is proportional to:
x
By analyzing the proportionality conditions, we find that (y + z - x) is proportional to x. Hence, the correct answer is (a) x.
Similar Questions
Let \(k\) be a positive integer. What is the quotient when \(x^{8k+3}+x^{8k+6}+x^{8k+9} + x^{8k+12}\) is divided by \((1+x^3)(1+x^6)\) ?
If 2s = a + b + c, then what is s(s-a)(s-b)(s-c) [ (1 / s-a) + (1 / s-b) + (1 / s-c) - (1 / s)] equal to?
- If \((x + 1)(x + p)(x^2 + p^2) = x^4 - 1\), then what is the value of \(p\)?
- If \((2+\sqrt{3})^x + (2-\sqrt{3})^x = 2\), then what is \((2+\sqrt{3})^x-(2-\sqrt{3})^x\) equal to?
What is
\(\frac{(a+b)^2}{(c-a)(c+a+b)} + \frac{(a+b)c}{c^2 + bc-a^2 - ab}\) - \(\frac{(a+2b + c)}{2(c-a)}\), \(a \neq b\), \(b \neq c\), \(c \neq a\)
equal to?
Which of the following is/are the factor(s) of \((3x + y)^2 + (3x+y)(x+5y)-20(x+5y)^2\)?
I. \((4x+13y)\)
II. \((x + 19y)\)
Select the correct answer using the code given below.
What is
\(\frac{\frac{x}{x-y}+\frac{y}{y-z}+\frac{z}{z-x}} {\frac{x+y}{x-y}+\frac{y+z}{y-z}+\frac{z+x}{z-x}+3}\)equal to?
- If $p = \sqrt[3]{a + \sqrt{a^2 + b^3}} + \sqrt[3]{a - \sqrt{a^2 + b^3}}$, then what is $p^3 + 3bp$ equal to ?
If \(x^3 + \frac{1}{x^3} = \frac{65}{8}\) and \(y^3 + \frac{1}{y^3} = \frac{730}{27}\), then which one of the following is a value of \(xy\)?
- What is HCF of
\(a^4+2a^3+3a^2+2a+1\) and \(a^6-2a^3+1\)?
Important Questions from Algebra
In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.
I. x2 – 26x + 165 = 0
II. y2 – 38y + 357 = 0
Factorize the following:
(x 2- 6xy + 9y 2) - 25
If P and Q are the points on the line Joining A(-2, 5) and B(3, 1) such that
AP = PQ = QB, then the mid point of PQ is
If a number and its reciprocal added it becomes 6, then what will be sum of its square and square of its reciprocal?
If 3x + 2y = 15, and xy = 6. Find the value of (3x3/2) + (4y3/9).
