Advertisements
Advertisements
प्रश्न
Solve `4x^2+4bx-(a^2-b^2)=0`
उत्तर
`4x^2+4bx-(a^2-b^2)=0`
⇒ `4x^2+4bx-(a-b)(a+b)=0`
⇒`4x^2+2[(a+b)-(a-b)]x-(a-b)(a+b)=0`
⇒`4x^2+2(a+b)x-2(a-b)x-(a-b)(a+b)=0`
⇒`2x[2x+(a+b)]-(a-b)[2x+(a+b)]=0`
⇒`[2x+(a+b)][2x-(a-b)]=0`
⇒`2x+(a+b)=0 or 2x-(a-b)=0`
⇒` x=(-a+b)/2` or ` x=(a-b)/2`
Hence, `-(a+b)/2` and `(a-b)/2` are the roots of the given equation.
APPEARS IN
संबंधित प्रश्न
(a) `3x-x^2=x^2+5` (b) `(x+2)^2=2(x^2-5)`
(c) `(sqrt2x+3)^2=2x^2+6` (d)` (x-1)^2=3x^2+x-2`
If the equation `9x^26kx+4=0` has equal roots then k =?
(a)1 or (b)-1 or 4 (c)1 or -4 (d)-1 or -4
If the roots of` 5x^2-k+1=0` are real and distinct then
(a)`-2sqrt5<k2<sqrt5` (b)` k>2sqrt5 ` only
(c)` k<-2sqrt5` (d) either `k>2sqrt5 or k<-2sqrt5`
If one zero of the polynomial `x^2-4x+1 is (2+sqrt3)` write the other zero.
If one root of the quadratic equation `3x^2-10x+k=0` is reciprocal of the other , find the value of k.
Solve `sqrt3x^2+10x-8sqrt3=0`
If 460 is divided by a natural number, quotient is 6 more than five times the divisor and remainder is 1. Find quotient and divisor.
Which is the following equation quadratic?
x2 + 2x + 11 = 0
Write the following equation in the form ax2 + bx + c= 0, then write the values of a, b, c for equation.
P(3+6p) = –5
In a right-angled triangle, altitude is 2 cm longer than its base. Find the dimensions of the right-angled triangle given that the length of its hypotenuse is 10 cm.
