Advertisements
Advertisements
प्रश्न
`x^2-(sqrt2+1)x+sqrt2=0`
उत्तर
`x^2-(sqrt2+1)x+sqrt2=0`
⇒`x^2-(sqrt2+1)x=-sqrt2`
⇒`x^2-2xx x xx((sqrt2+1)/2)+((sqrt2+1)/2)^2=sqrt2+((sqrt2+1)/2)^2`
[Adding `((sqrt2+1)/2)]^2` on the sides]
⇒`[x-((sqrt2+1)/2)]^2=(-4sqrt2+2+1+2sqrt2)/4=(2-2sqrt2+1)/4=((sqrt2-1)/2)^2`
⇒`x-((sqrt2+1)/2)=+-((sqrt2-1)/2)` (Taking square root on both sides)
⇒`x-((sqrt2+1)/2)=((sqrt2-1)/2) or x-((sqrt2-1)/2)=-((sqrt2-1)/2)`
⇒`x=(sqrt2+1)/2+(sqrt2-1)/2 or x=(sqrt2+1)/2-(sqrt2-1)/2`
⇒`x=(2sqrt2)/2=sqrt2 or x=2/2=1`
Hence, `sqrt2 and 1` are the roots of the given equation.
APPEARS IN
संबंधित प्रश्न
Find the roots of the quadratic equation 4x2 + 4√3x + 3 = 0
Find the roots of the quadratic equations 2x2 + x – 4 = 0 by applying the quadratic formula.
Two taps running together can fill a tank in `3 1/13` hours. If one tap takes 3 hours more than the other to fill the tank, then how much time will each tap take to fill the tank?
`sqrt2x^3-3x-2sqrt2=0`
A farmer prepares rectangular vegetable garden of area 180 sq meters. With 39 meters of barbed wire, he can fence the three sides of the garden, leaving one of the longer sides unfenced. Find the dimensions of the garden.
The area of a right triangle is `600cm^2` . If the base of the triangle exceeds the altitude by 10 cm, find the dimensions of the triangle.
The area of right-angled triangle is 96 sq meters. If the base is three time the altitude, find the base.
The ratio of the sum and product of the roots of the equation `7x^2-12x+18=0` is
(a) 7:12 (b)7:18 (c)3:2 (d)2:3
Solve the following quadratic equation by completing the square method.
x2 + 2x – 5 = 0
The sum of the areas of two squares is 400 sq.m. If the difference between their perimeters is 16 m, find the sides of two squares.
