Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced 2012Paper 1
Exam
JEE Advanced
Year
2012
Paper
Paper 1
Subject
Mathematics
Chapter
Quadratic Equation

JEE Advanced 2012 · Paper 1 · Mathematics · Quadratic Equation

The value of 6+ _ (3)/(2) ( 1 3 2 4- 1 3 2 4- 1 3 2 4- 1 3 2 ) is

The value of 6+log⁡32(1324−1324−1324−132⋯) is  6+\log _{\frac{3}{2}}\left(\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}}} \cdots}}\right) \text{\text{ is } }

Correct answer

0

Step-by-step solution

Let x=1324−1324−1324−132……⇒x=1324−x⇒32x=4−xx=\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}}}}} \ldots \ldots \Rightarrow \quad x=\frac{1}{3 \sqrt{2}} \sqrt{4-x} \Rightarrow \quad 3 \sqrt{2} x=\sqrt{4-x}⇒18x2=4−x⇒18x2+x−4=0⇒(9x−4)(2x+1)=0⇒x=49 or x=−12\begin{array}{l} \Rightarrow \quad 18 x^{2}=4-x \\ \Rightarrow \quad 18 x^{2}+x-4=0 \\ \Rightarrow \quad(9 x-4)(2 x+1)=0 \\ \Rightarrow \quad x=\frac{4}{9} \text{ or } x=-\frac{1}{2} \end{array}(Notpossiblebecauselogisnotdefinefor−vevalue)(Not possible because log is not define for -ve value)\begin{aligned} \therefore \quad & 6+\log _{\frac{3}{2}}\left(\frac{4}{9}\right)=6+\log _{\frac{3}{2}}\left(\frac{3}{2}\right)^{-2} \\ &=6-2=4 \end{aligned}$$
Practice Quadratic Equation on Quantrex Academy →

More from Quadratic Equation

Match each entry in List-I to the correct entry in List-II and choose the correct option.… JEE Advanced 2026Let a, b, c be positive integers in arithmetic progression such that the equation ax^2 +… JEE Advanced 2026Consider the quadratic equation (n^2 - 2n + 2)x^2 - 3x + (n^2 - 2n + 2)^2 = 0 , n ∈ ℝ .… JEE Main 2026Let one root of the quadratic equation in x : (k^2 - 15k + 27)x^2 + 9(k-1)x + 18 = 0 be… JEE Main 2026Let e_1 and e_2 be two distinct roots of the equation x^2 - ax + 2 = 0 . Let the sets \ a… JEE Main 2026Let α, β be the roots of the equation x^2 - x + p = 0 and γ, δ be the roots the equation… JEE Main 2026Let a, b ∈ ℂ . Let α, β be the roots of the equation x^2 + ax + b = 0 . If β - α = 11 and… JEE Main 2026Let A, B , where A, B ∈ (-(π)/(2), (π)/(2)) , be the roots of the quadratic equation x^2… JEE Main 2026If α=1 and β=1+i 2 , where i= -1 are two roots of the equation x^3+ax^2+bx+c=0 , a,b,c ∈… JEE Main 2026If the quadratic equation (λ+2)x^2-3λ x+4λ=0 , λ ≠ -2 , has two positive roots, then the… JEE Main 2026Let α, β be the roots of the equation x^2 - 3x + r = 0 , and (α)/(2), 2β be the roots of… JEE Main 2026Let a, b, c ∈ \ 1, 2, 3, 4\ . If the probability, that ax^2 + 2 2 \,bx + c > 0 for all x… JEE Main 2026Let S=\ x^ 3 +a x^ 2 +b x+c: a, b, c ∈ ~N. and .a, b, c ≤ 20\ be a set of polynomials.… JEE Main 2026If α, β , where α<β , are the roots of the equation λ x^ 2 -(λ+3) x+3=0 such that… JEE Main 2026The smallest positive integral value of a , for which all the roots of x^ 4 -a x^ 2 +9=0… JEE Main 2026The sum of all the real solutions of the equation _ (x+3) (6 x^ 2 +28 x+30)=5-2 _ (6… JEE Main 2026 Full Quadratic Equation list Quadratic Equation JEE Maths PYQsJEE Mathematics PYQs All JEE Advanced PYQs