Algebra

Quantitative Aptitude and Numerical Ability (DRDO) (Phase-i and II)

Title

45:30

8 of 24 completed

5 of 15 completed

38 of 100 completed

8 of 20 completed

Indian Economy - Understanding the basics of Indian economic system

If x+y+z=10, x²+y²+z²=38, x³+y³+z³=160 then find the value of XYZ?

x+y+z=10

x^2+y^2+z^2=38

Now,we have a formulae -(x+y+z)^2=x^2+y^2+z^2+2(xy+yz+zx)

Putting known values in above formulae,we get

100=38+2(xy+yz+zx) or (xy+yz+zx)=62/2=31

Now,we are also given with x^3+y^3+z^3=160

We have a formulae -

x^3+y^3+z^3–3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)

Putting known values in above equation,we get

160–3xyz=(10)(38–31) {Since,we have already got the value of xy+yz+zx}

160–3xyz=70 or 3xyz=90 or xyz=30

Thus,value of xyz=30

Hence, option 2 is the correct answer.