Advertisements
Advertisements
प्रश्न
Solve the following equation by factorization
`sqrt(x(x - 7)) = 3sqrt(2)`
Advertisements
उत्तर
`sqrt(x(x - 7)) = 3sqrt(2)`,
Squaring both sides,
x(x - 7) = 9 x 2
⇒ x2 - 7x = 18
⇒ x2 - 7x - 18 = 0,
⇒ x2 - 9x + 2x - 18 = 0
⇒ x(x - 9) + 2(x - 9) = 0
⇒ (x - 9) (x + 2) = 0
Either x - 9 = 0,
then x = 9
or
x + 2 = 0,
then x = -2
∴ x = 9, -2
check
(i) If x = 9, then
L.H.S.
= `sqrt(x(x - 7)`
= `sqrt(9(9 - 7)`
= `sqrt(9 xx 2)`
= `sqrt(18)`
= `sqrt(9 xx 2)`
= `3sqrt(2)`
= R.H.S.
x = 9 is a root
(ii) If x = -2, then
L.H.S.
= `sqrt(x(x - 7)`
= `sqrt(-2(-2 - 7)`
= `sqrt(-2 xx -9)`
= `sqrt(18)`
= `sqrt(9 xx 2)`
= `3sqrt(2)`
= R.H.S.
∴ x = -2 is also its root
Hence x = 9, -2.
APPEARS IN
संबंधित प्रश्न
Solve for x : 12abx2 – (9a2 – 8b2 ) x – 6ab = 0
A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
Solve the following quadratic equations by factorization:
9x2 − 3x − 2 = 0
A passenger train takes 3 hours less for a journey of 360 km, if its speed is increased by 10 km/hr from its usual speed. What is the usual speed?
The hypotenuse of a right triangle is `3sqrt10`. If the smaller leg is tripled and the longer leg doubled, new hypotenuse wll be `9sqrt5`. How long are the legs of the triangle?
Solve for x: `3x^2-2sqrt3x+2=0`
Find the value of k for which the following equations have real and equal roots:
\[x^2 - 2\left( k + 1 \right)x + k^2 = 0\]
Find the values of k for which the roots are real and equal in each of the following equation:
\[kx\left( x - 2\sqrt{5} \right) + 10 = 0\]
A two digit number contains the bigger at ten’s place. The product of the digits is 27 and the difference between two digits is 6. Find the number.
If x = –2 is the common solution of quadratic equations ax2 + x – 3a = 0 and x2 + bx + b = 0, then find the value of a2b.
