Solving System of Equations with Square Roots: Find ab

Published on February 24, 2026

Algebra

Solve the system of equations sqrt(a+b)=5 and sqrt(a-b)=5 to find the value of ab. This involves squaring both sides and solving the resulting linear equations.

Question

Answer

Okay, let’s solve this system of equations step by step.

The given equations are:

Squaring both sides of each equation, we get:

Now we have a system of two linear equations with two variables. We can solve this system by adding the two equations:

Now, substitute the value of

into either equation to find

. Let’s use the first equation:

Finally, we need to find the value of

Therefore,

Final Answer: The final answer is

🚀 Try Free Math Help Now!🏠 Learn More Powerful Features

Related math solutions

Finding Reflections Across the Axis of Symmetry

Learn how to find the reflections of given coordinate points across the vertical axis of symmetry x = -3 using horizontal distance formulas.

Identifying Systems of Inequalities from Graphs: Parabola and Absolute Value

This problem involves determining the correct system of inequalities based on a graph showing a shaded region bounded by a solid parabola and a dashed absolute value function. The solution requires analyzing the line types (solid vs. dashed) to determine strict or non-strict inequalities and identifying the equations of the boundary curves.

Solve Change Problem Quadratic Equation and Fractions Step by Step

Learn how to calculate shopping change, solve a quadratic equation using the quadratic formula, and evaluate fraction operations with clear step-by-step explanations.

Solve Rational Equation (y-1)/(1-y)=1

Determine that the rational equation (y-1)/(1-y)=1 has no solution because the denominator is the negative of the numerator, making the left side equal -1.

Prove Re(z+1)/(z-1) = 0 for Complex Number Magnitude 1

Learn how to prove that the real part of the complex expression (z+1)/(z-1) is equal to zero when |z|=1 and z is not equal to 1, using complex conjugates and magnitude properties.

🔎 Explore All Shared Math Solutions