Question 1
If p-q = 9, and $$p^{2} + q^{2} = 127$$. Find the value of pq.
SSC Quadratic Equations Questions
SSC Quadratic Equations Questions
Question 1
$$x (5 - \frac{2}{x}) = \frac{5}{x}$$, then the value of $$x^{2} + \frac{1}{x^{2}}$$ is:
Question 2
If $$4x^{2} + y^{2} = 40$$ and xy = 6, then find the value of 2x + y
Question 1
What is the LCM of ($$8x^{3} + 80x^{2} + 200x$$) and ($$4x^{4} + 16x^{3} - 20x^{2}$$)?
Solution
$$8x^{3} + 80x^{2} + 200x$$ can be factorized as $$8x\left(x+5\right)^2$$.
$$4x^{4} + 16x^{3} - 20x^{2}$$ can be factorized as $$4x^2\left(x+5\right)\left(x-1\right)$$.
The LCM will be $$8x^2\left(x+5\right)^2\left(x-1\right)$$.
Question 1
If $$(x - 3)^2 + (2x - 5)^3 + (x - 4)^3 = (3x - 9)(2x - 5)(x - 4)$$ , then what is the value of $$x$$ ?
Solution
The best way to solve such questions is by substituting the options given :
On substituting x=3
we get LHS = 0
And RHS =0
so we get x=3
Question 2
If $$(x - 5)^3 + (x - 6)^3 + (x - 7)^3 = 3 (x - 5) (x - 6) (x - 7)$$, then what is the value of $$x$$?
Question 3
$$p^3 + q^3 + r^3 - 3pqr = 4$$. If $$a = q + r, b = r + p$$ and $$c = p + q$$, then what is the value of $$a^3 + b^3 + c^3 - 3abc$$?
Question 4
If $$a^3 - b^3 = 3552$$ and $$(a - b) = 6$$, then $$(a + b)^2 - ab$$ is equal to:
Question 5
If $$(2x+3)^3+(x-8)^3+(x+13)^3=(2x+3)(3x-24)(x+13)$$, then what is the value of $$x$$ ?
Question 6
If $$(x + 4)^3 + (2x + 1)^3 + (2x + 5)^3 = (3x+ 12)(2x + 1)(2x + 5)$$, then what is the value of $$x$$?
Question 7
If $$x^4 + 2x^3 + ax^2 + bx + 9$$ is a perfect square, where a and b are positive real numbers,then the value of a and b are
