V1-v2-4 and v21-v22-16- Find value of v1 and v2-

228

You visited us 228 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Solving a Quadratic Equation by Completion of Squares Method

v1+v2=4 and ...

Question

$v_{1} + v_{2} = 4$ and $v_{1}^{2} + v_{2}^{2} = 16$ . Find value of $v_{1}$ and $v_{2}$ .

Open in App

Solution

$v_{1} + v_{2} = 4$
$v_{1} = 4 - v_{2}$

substitute $v_{1} = 4 - v_{2}$ in the second equation.

${v_{1}}^{2} + {v_{2}}^{2} = 16$

${4 - v_{2}}^{2} + {v_{2}}^{2} = 16$

$16 + {v_{2}}^{2} - 8 v_{2} + {v_{2}}^{2} = 16$

${v_{2}}^{2} - 8 v_{2} + {v_{2}}^{2} = 0$

$2 {v_{2}}^{2} - 8 v_{2} = 0$

${v_{2}}^{2} - 4 v_{2} = 0$

$v_{2} (v_{2} - 4) = 0$

$v_{2} - 4 = 0$

$v_{2} = 4$

now, substitute $v_{2} = 4$ in first equation.

$v_{1} + 4 = 4$

$v_{1} = 0$

so, $v_{1} = 0$ and $v_{2} = 4$ or $v_{1} = 4$ and $v_{2} = 0$

Suggest Corrections

Similar questions

Q. In the shown figure, block moves downwards with velocity

v_{1}

, the wedge moves rightwards with velocity

v_{2}

. The correct relation between

v_{1}

and

v_{2}

The driver of a train moving with a constant velocity v₁along a straing track sights another train at a distance d ahrad of him on the same track moving in a same direction with a constant speed V2. He at once applies a brakes and gives his train a constant retardation f. There will be a collosioc of yhe trains if......?

a) v1 > V2 amd (V1 -V2)²/2f < d

b) V1<V2 and (V1+V2)² /2f > d

c) V1 > V2 and ( V1-V2)²/2f > d

d) V1>V2 and (V1²- V2²)/2f > d

A car decelerates uniformly from velocity v₁ to velocity v₂ while getting displaced by s. If the diameter of the wheel is d, the angular acceleration of the wheel is

A person travels along a straight road for half the distance with velocity $v_{1}$ and the remaining half distance with velocity $v_{2}$ The average velocity is given by

Two identical photo-cathodes receive light of frequencies $f_{1} a n d f_{2}$ . If the velocities of the photo electrons (of mass m) coming out are respectively $v_{1} a n d v_{2}$ , then

Join BYJU'S Learning Program

v1+v2=4 and v21+v22=16. Find value of v1 and v2.

v1+v2=4v1=4−v2substitute v1=4−v2 in the second equation.v12+v22=164−v22+v22=1616+v22−8v2+v22=16v22−8v2+v22=02v22−8v2=0v22−4v2=0v2(v2−4)=0v2−4=0v2=4now, substitute v2=4 in first equation.v1+4=4v1=0so, v1=0 and v2=4 or v1=4 and v2=0

$v_{1} + v_{2} = 4$ and $v_{1}^{2} + v_{2}^{2} = 16$ . Find value of $v_{1}$ and $v_{2}$ .