left(1right)x^2-sqrt2x+frac12=0,because a=1,b=-sqrt2,c=frac12,therefore Delta =b^2-4ac=2-4times 1times frac12=0,方程有两个相等的实数根,therefore x=frac(-b±sqrt(b^2-4ac))(2a)=frac(sqrt2)2,therefore x_1=x_2=frac(sqrt2)2;(2)4x^2-3x+2=0,because a=4,b=-3,c=2...
解:要使二次根式\sqrt{2-3x}有意义,需要2-3x\geqslant 0,解得:x\leqslant\dfrac{2}{3}.故答案是:x\leqslant\dfrac{2}{3}.根据被开方数大于等于0列式计算即可得解.考查了二次根式的意义和性质.概念:式子\sqrt{a}(a\geqslant 0)叫二次根式.性质:二次根式中的被开方数必须是非负数,否则二次根式无意...
Evaluate:(Lim)x→4√2x+1+√x−3−4√(3x+4)+√5x+5−9 View Solution Evaluate the following limit:(lim)x→±∞(√x2−2x−1−√x2−7x−3) View Solution Evaluatelimx→0√1+x3−√1−x3x2 View Solution Evaluate:(lim)x→∞x3{√x2+√1+x4−x√2} ...
Simplify the equation. 2x + 3y + 2(x - y) - 3x Simplify the equation: 7 x - 4 x - x 12 Simplify the equation. -4x / (x - x^2) Simplify: \frac{6}{5x} - \frac{5}{x - 2} Simplify: \frac{x^2 + 2x - 63}{x^2 +3x - 70}\times\frac{x^2 -6x -40}{x^2 + ...
(d)/(dx) {(1)/(sqrt(3x +2))}= 02:12 If y = sqrt(ax) + (a ^(2))/(sqrt(ax))then y (1) , y (2) at x =a are 05:37 The derivative of sqrt(sin x + sqrt(sin x )) w.r.t x is 03:38 The derivative of sqrt(tan x + sqrt(tan x )) w.r.t x is 03:48 ...
应用立方根的性质解决下列问题:(1)若sqrt[3](1-a^2)=1-a^2,求a的值.(2)若sqrt[3](1-2x)与sqrt[3](3x-5)互为相反数,求1-
解析 (1)原式=2sqrt3+3-sqrt3-3=sqrt3;(2)left(begin(array)l(2x+3y=13①)\(3x+1=y+4②)end(array)right.,由②得:y=3x-3③,将③代入①得2x+9x-9=13,解得x=2,将x=2代入③得:y=3,therefore 原方程的解为left(begin(array)l(x=2)\(y=3)end(array)right.....
View Solution Solve for x : √3x2+14x−5√3=0 View Solution Doubtnut is No.1 Study App and Learning App with Instant Video Solutions for NCERT Class 6, Class 7, Class 8, Class 9, Class 10, Class 11 and Class 12, IIT JEE prep, NEET preparation and CBSE, UP Board, Bihar Board...
Let $$\alpha=\sqrt{6}\ \sqrt{12+7\,\sqrt3}-3\,\sqrt3-6\,=\,\big(2+\sqrt{3}\big) \big(\sqrt{2} \sqrt[4]{27}-3\big)\,=\,\frac{3\sqrt{3}}{3+\sqrt2\ \sqrt[4]{27}}.\tag1$$ Note that $\alpha$ is the unique positive root of the polynomi...
View Solution (1+√2√5+√3+1−√2√5−√3)Simplify View Solution Doubtnut is No.1 Study App and Learning App with Instant Video Solutions for NCERT Class 6, Class 7, Class 8, Class 9, Class 10, Class 11 and Class 12, IIT JEE prep, NEET preparation and CBSE, UP Board, Biha...