Home
Class 9
MATHS
If x=(sqrt(a+2b)+sqrt(a-2b))/(sqrt(a+2b)...

If `x=(sqrt(a+2b)+sqrt(a-2b))/(sqrt(a+2b)-sqrt(a-2b))`, then prove that `b ^2-ax+b=0`

Text Solution

Verified by Experts

We have, `x=(sqrt(a+2b)+sqrt(a-2b))/(sqrt(a+2b)-sqrta-2b)=(sqrt(a+2b)+sqrt(a-2b))/(sqrt(a+2b)-sqrta-2b)xx(sqrt(a+2b)+sqrt(a-2b))/(sqrt(a+2b)-sqrta-2b)`
`=((sqrt(a+2b)+sqrt(a-2b))^(2))/((sqrt(a+2b)-sqrta-2b)^(2))=(a+2b+a-2b+2sqrt((a+2b)(a-2b)))/((a+2b)-(a-2b))`
`(2a+2sqrt(a^(2)-4b^(2)))/(4b)rArr" "x=(a+sqrt(a^(2)-4b^(2)))/(2b)`
`rArr" "2bx=a+sqrt(a^(2)-4b^(2))" "rArr2bx-a=sqrt(a^(2)-4b^(2))`
Squaring both sides, we get
`=(2bx-a)^(2)=a^(2)-4b^(2)`
`=4b^(2)x^(2)+a^(2)-4abx=a^(2)-4b^(2)`
`=4b^(2)x^(2)-4abx+4b^(2)=0`
`rArr" "4b(bx^(2)-ax+b)=0`
`:." either "b=0orbx^(2)-ax+b=0`
But b cannot be zero as it will not give the real value of x.
`:." "bx^(2)-ax+b=0`
Promotional Banner

Topper's Solved these Questions

  • NUMBER SYSTEM

    NAGEEN PRAKASHAN ENGLISH|Exercise Problems From NCERT/exemplar|7 Videos

  • NUMBER SYSTEM

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 1a|5 Videos

  • LINES AND ANGLES

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise (long Answer Questions )|6 Videos

  • POLYNOMIALS

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise (short Answer Questions)|16 Videos

Similar Questions

Explore conceptually related problems

if x = (sqrt(3a + 2b) + sqrt(3a - 2b))/(sqrt(3a + 2b) - sqrt(3a - 2b)) prove that : bx^(2) - 3ax + b = 0

If x = (sqrt(a + 3b) + sqrt(a - 3b))/ (sqrt(a + 3b) - sqrt(a - 3b)) prove that : 3bx^(2) - 2ax + 3b = 0 .

If y=((a-x)sqrt(a-x)-(b-x)sqrt(x-b))/((sqrt(a-x)+sqrt(x-b)) ,then (dy)/(dx) wherever it is defined is (a) (x+(a+b))/(sqrt((a-x)(x-b))) (b) (2x-a-b)/(2sqrt(a-x)sqrt(x-b)) (c) -((a+b))/(2sqrt((a-x)(x-b))) (d) (2x+(a+b))/(2sqrt((a-x)(x-b)))

If cosA/2=sqrt((b+c)/(2c)) , then prove that a^2+b^2=c^2dot

Given x = (sqrt(a^(2) + b^(2)) + sqrt(a^(2) - b^(2)))/(sqrt(a^(2) + b^(2)) - sqrt(a^(2) - b^(2))) . Use componendo and dividendo to prove that : b^(2) = (2a^(2)x)/(x^(2) + 1) .

If sum_(k = 1)^(oo) (1)/((k + 2)sqrt(k) + ksqrt(k + 2)) = (sqrt(a) + sqrt(b))/(sqrt(c)) , where a, b, c in N and a,b,c in [1, 15] , then a + b + c is equal to

If a=(2-sqrt(5))/(2+sqrt(5)) and b=(2+sqrt(5))/(2-sqrt(5)), find a^2-b^2

If a=(2-sqrt(5))/(2+sqrt(5)) and b=(2+sqrt(5))/(2-sqrt(5)), find a^2-b^2

If the equation ax^2+2hxy+by^2+2gx+2fy+c=0 represents a pair of parallel lines, prove that h=sqrt(ab) and gsqrt(b)=fsqrt(a)or (h=-sqrt(ab)and gsqrt(b)=-fsqrt(a)) . The distance between them is 2sqrt((((g^2-ac))/(a(a+b)))) .

If (sqrt(3)-\ 1)/(sqrt(3)+\ 1)=a-b\ sqrt(3) , then (a) a=2,\ b=1 (b) a=2,\ b=-1 (c) a=-2,\ b=1 (d) a=b=1