Number Systems - Question 4 || 9&10 Math Capsule || Misbah Sir || Infinity Learn Class 9&10

TL;DR

By adding and completing the square of three equations, we can find that x square plus y square plus Z Square equals 14.

Transcript

hello everybody so here we have got a question on the basics of real numbers and you have to find the value of x square plus y square plus Z Square so all these three equations it will waste your time maybe we'll be able to do it but it will base your time there is a trick in this question basically so let us add these three questions and let's see... Read More

Key Insights

• 🟨 The trick used in this question involves adding and completing the square of three equations to find the value of x square plus y square plus Z Square.
• 😃 The equations are simplified by rewriting them in the form of a plus b the whole Square identity.
• 😑 The resulting expression is set equal to zero and the values of x, y, and Z can be determined accordingly.

Questions & Answers

Q: How can we find the value of x square plus y square plus Z Square based on the given equations?

By adding the equations together and completing the square, we can simplify the expression and find that x square plus y square plus Z Square equals 14.

Q: Why is it more efficient to use the trick rather than solving the equations individually?

Solving the equations individually would be time-consuming and may lead to errors. The trick of adding and completing the square allows for a quicker and more efficient solution.

Q: How do we complete the square in this problem?

To complete the square, we add the square of half the coefficient of each variable term to both sides of the equation. This helps rewrite the equation in the form of a plus b the whole Square identity.

Q: How do we determine the values of x, y, and Z based on the solution?

By setting the expressions within the parentheses of the completed squares equal to zero, we can solve for x, y, and Z. In this case, x equals -1, y equals -3, and Z equals -2.

Summary & Key Takeaways

• The question involves finding the value of x square plus y square plus Z Square based on three given equations.

• Solving the equations individually would be time-consuming, so a trick is used to simplify the process.

• By adding the equations and completing the square, it is determined that x square plus y square plus Z Square equals 14.